Showing papers in "IEEE Transactions on Circuits and Systems I-regular Papers in 1998"
TL;DR: The theory of conventional telecommunications is extended to chaotic communications, chaotic modulation techniques and receiver configurations are surveyed, and chaotic synchronization schemes are described.
Abstract: For pt. I see ibid., vol. 44, p. 927-36 (1997). In a digital communications system, data are transmitted from one location to another by mapping bit sequences to symbols, and symbols to sample functions of analog waveforms. The analog waveform passes through a bandlimited (possibly time-varying) analog channel, where the signal is distorted and noise is added. In a conventional system the analog sample functions sent through the channel are weighted sums of one or more sinusoids; in a chaotic communications system the sample functions are segments of chaotic waveforms. At the receiver, the symbol may be recovered by means of coherent detection, where all possible sample functions are known, or by noncoherent detection, where one or more characteristics of the sample functions are estimated. In a coherent receiver, synchronization is the most commonly used technique for recovering the sample functions from the received waveform. These sample functions are then used as reference signals for a correlator. Synchronization-based coherent receivers have advantages over noncoherent receivers in terms of noise performance, bandwidth efficiency (in narrow-band systems) and/or data rate (in chaotic systems). These advantages are lost if synchronization cannot be maintained, for example, under poor propagation conditions. In these circumstances, communication without synchronization may be preferable. The theory of conventional telecommunications is extended to chaotic communications, chaotic modulation techniques and receiver configurations are surveyed, and chaotic synchronization schemes are described.
474 citations
TL;DR: Simulation results show the utility of the unified design approach based on LMIs proposed in this paper, and the chaotic model following control problem, which is more difficult than the synchronization problem, is discussed using the EL technique.
Abstract: This paper presents a unified approach to controlling chaos via a fuzzy control system design based on linear matrix inequalities (LMI's). First, Takagi-Sugeno fuzzy models and some stability results are recalled. To design fuzzy controllers, chaotic systems are represented by Takagi-Sugeno fuzzy models. The concept of parallel distributed compensation is employed to determine structures of fuzzy controllers from the Takagi-Sugeno fuzzy models, LMI-based design problems are defined and employed to find feedback gains of fuzzy controllers satisfying stability, decay rate, and constraints on control input and output of fuzzy control systems. Stabilization, synchronization, and chaotic model following control for chaotic systems are realized via the unified approach based on LMIs. An exact linearization (EL) technique is presented as a main result in the stabilization. The EL technique also plays an important role in the synchronization and the chaotic model following control. Two cases are considered in the synchronization. One is the feasible case of the EL problem. The other is the infeasible case of the EL problem. Furthermore, the chaotic model following control problem, which is more difficult than the synchronization problem, is discussed using the EL technique. Simulation results show the utility of the unified design approach based on LMIs proposed in this paper.
373 citations
TL;DR: In this paper, the A-switching map is introduced, which is related to the asynchronous switchings, i.e., the changes of converter configuration occurring within the modulating period.
Abstract: Nonlinear phenomena in closed-loop pulsewidth modulated (PWM) DC/DC converters are analyzed. We introduce a new discrete time nonlinear map-the A-switching map-which is related to the asynchronous switchings, i.e., the changes of converter configuration occurring within the modulating period. This map is compared with the stroboscopic map, which is typically used in the study of DC/DC converters. Analytical conditions for the occurrence of periodic orbits and flip bifurcations are obtained. Moreover, necessary conditions for infinite local stretching on the phase space are derived. Finally, a possible explanation of the sudden jump to chaos exhibited by DC/DC converters is proposed. Analytical and numerical results can be applied to all fundamental DC/DC converter topologies. The case of the voltage-controlled buck converter is treated in detail.
264 citations
TL;DR: In this paper, the identification of RC networks from their time or frequency-domain responses is carried out by deconvolution (NID method), where all response functions are calculated by convolution integrals.
Abstract: This paper deals with the identification of RC networks from their time- or frequency-domain responses. A new method is presented based on a recent approach of the network description where all response functions are calculated by convolution integrals. The identification is carried out by deconvolution (NID method). This paper discusses the practical details of the method. Special attention is paid to the identification and modeling of distributed RC networks, like the problems of conductive heat-flow. A number of examples make it easy to understand the operation and the capabilities of the NID method. Comparative considerations are given concerning the accuracy and expenses of the NID and the popular AWE (momentum-matching) methods.
246 citations
TL;DR: In this article, a method of predicting the local bifurcation structure through the construction of a normal form is applied to many power electronic circuits as well as other piecewise smooth systems.
Abstract: Interesting bifurcation phenomena are observed for the current feedback-controlled buck converter. We demonstrate that most of these bifurcations can be categorized as "border-collision bifurcations." A method of predicting the local bifurcation structure through the construction of a normal form is applied. This method applies to many power electronic circuits as well as other piecewise smooth systems.
243 citations
TL;DR: In this article, an electrical power network consisting of generators and transmission lines is treated as a continuum system, and the application of the limit of zero generator spacing, with finite rotor inertia and transmission line impedance per unit length, yields a nonlinear partial differential equation in time and two spatial dimensions for the rotor phase angle.
Abstract: An electrical power network consisting of generators and transmission lines is treated as a continuum system. The application of the limit of zero generator spacing, with finite rotor inertia and transmission line impedance per unit length, yields a nonlinear partial differential equation in time and two spatial dimensions for the rotor phase angle. The equation is a nonlinear version of the standard second-order wave equation which exhibits an explicit expression for the finite wave phase velocity. The electromechanical wave propagation characteristics, equilibrium solutions, and linear stability are investigated and some potentially important results are presented. Numerical simulations of the usual discrete generator model, based upon the swing equation, are presented and demonstrate the electromechanical wave propagation as having interesting properties. Numerical solutions of the analogous continuum model are compared to the discrete model and are found to be in excellent agreement. A numerical estimate of the wave phase velocity for the U.S. power grid is consistent with observations of the transient wave phenomena during staged fault events. The continuum model enables an array of alternative analytic and simulation methods to be applied to the study of global power system characteristics, such as stability and transient dynamics.
217 citations
TL;DR: In this paper, a robust linear decentralized controller is proposed to enhance the transient stability of nonlinear multimachine power systems, which is based on solving an algebraic Riccati equation based on the bounds of the machine parameters.
Abstract: In this paper, a new robust linear decentralized controller is proposed to enhance the transient stability of nonlinear multimachine power systems. Only local measurements are required in the proposed controller. The feedback gain of each generator is obtained by solving an algebraic Riccati equation based on the bounds of the machine parameters. The stability analysis shows that the decentralized controller can guarantee the system stability over the whole operating region and regardless of fault locations or parameter uncertainties of the transmission network. Compared with nonlinear controllers, linear controllers are of simpler structure and easier to be implemented. A three-machine power system is considered as an application example. Simulation results show that despite the interconnections between different generators, nonlinearities in the system, different operating points, and different fault locations, the proposed robust decentralized controller can greatly enhance power system transient stability.
186 citations
TL;DR: In this article, a sufficient condition for the uniqueness and global asymptotic stability of the equilibrium point of DCCNs with delay was given. But the stability properties of the stability point are not affected by the delay parameter, which is weaker than some previously given for global stability of DCNNs.
Abstract: The authors present two new results on the global stability of cellular neural networks with delay (DCCNs). First, a sufficient condition for the uniqueness and global asymptotic stability of the equilibrium point is given. Then, a sufficient condition for the existence of a stable equilibrium point in the total saturation region is obtained. The significance of the conditions is that the stability properties of the equilibrium point are not affected by the delay parameter. These conditions are also weaker than some previously given for global stability of DCNNs.
182 citations
TL;DR: Mazzini et al. as discussed by the authors evaluated the impact of chaotic spreading codes on communication systems with asynchronous Code Division Multiple Access (CDMA) and provided analytical bounds on the expected partial cross correlation between spreading sequences obtained by quantizing and repeating a chaotic time series.
Abstract: For pt.I see G. Mazzini et al., vol.44, pp.937-47 (Oct. 1997). This paper and its companion (Part I) are devoted to the evaluation of the impact of chaos-based techniques on communications systems with asynchronous Code Division Multiple Access. In Part I, a performance index was introduced and exploited to a priori estimate the performance of DS-CDMA communications systems based on chaotic spreading sequences, and to compare it to that of conventional systems. Here, tools from nonlinear dynamical system theory are employed to give a formal ground for those results. Analytical bounds on the expected partial cross correlation between spreading sequences obtained by quantizing and repeating a chaotic time series are derived, ensuring general applicability of such a technique in a real environment. Further analytical arguments guarantee that, when particular chaotic generators are used, expected performance is not worse than that of a well-behaving communications system. This analysis ensures also that, unlike conventional sequences, chaotic spreading codes can be generated for any number of users and allocated bandwidth.
154 citations
TL;DR: In this paper, the design of on-chip decoupling capacitance and modeling of resonance effects in the power supply network of CMOS integrated circuits is addressed, based on mathematical limits proving that damping will be low, resulting in resonance.
Abstract: Design of on-chip decoupling capacitance and modeling of resonance effects in the power supply network of CMOS integrated circuits is addressed. The modeling is based on mathematical limits proving that damping will be low, resulting in resonance unless careful design is used. Design strategies that reduce resonance are discussed. It is shown that an optimal parasitic resistor in series with the decoupling capacitor gives a maximum damping factor of 0.5 and practical values are within the range 0.3-0.4. Examples of digital circuits show that proper design of on-chip decoupling capacitance may reduce the number of bonding wires by an order of magnitude. The modeling and design suggestions are also applicable to mixed-mode circuits. In particular, sampled analog networks benefit with a potentially higher sampling rate if enhanced damping is introduced during design.
141 citations
TL;DR: In this paper, the authors present a new methodology to calculate parameters of a nonlinear system, so that its distance to a saddle-node bifurcation is maximized with respect to the particular parameters that drive the system to bifurlcation.
Abstract: This paper presents a new methodology to calculate parameters of a nonlinear system, so that its distance to a saddle-node bifurcation is maximized with respect to the particular parameters that drive the system to bifurcation. The technique is thoroughly justified, specifying the conditions when it can be applied and the numeric mechanisms to obtain the desired solutions. A comparison is also carried out between the proposed method and a known methodology to determine closest saddle-node bifurcations in a particular power system model, showing that the new technique is a generalization of the previous method. Finally, applications to power systems are discussed, particularly regarding the design of some FACTS devices, and a simple generator-line-load example is studied to illustrate the use of the proposed technique to determine the optimal shunt and/or series compensation to maximize distances to voltage collapse. The effect of the optimal compensation on the stability of the sample system is also analyzed.
TL;DR: In this article, the authors present a new sufficient condition for global asymptotic stability of Lur'e systems with sector and slope restricted nonlinearities, expressed as a matrix inequality.
Abstract: In this brief we present a new sufficient condition for global asymptotic stability of Lur'e systems with sector and slope restricted nonlinearities. It is expressed as a matrix inequality and is based on an extended Lur'e-Postnikov Lyapunov function. It is compared based on numerical examples to conditions of Josselson-Raju and Haddad-Kapila.
TL;DR: A spatial subband image-compression method well suited to the local nature of the CNNUM, which performs especially well with radiographical images (mammograms) and is suggested to use as part of a cellular neural/nonlinear (CNN)-based mammogram-analysis system.
Abstract: This paper demonstrates how the cellular neural-network universal machine (CNNUM) architecture can be applied to image compression. We present a spatial subband image-compression method well suited to the local nature of the CNNUM. In case of lossless image compression, it outperforms the JPEG image-compression standard both in terms of compression efficiency and speed. It performs especially well with radiographical images (mammograms); therefore, it is suggested to use it as part of a cellular neural/nonlinear (CNN)-based mammogram-analysis system. This paper also gives a CNN-based method for the fast implementation of the moving pictures experts group (MPEG) and joint photographic experts group (JPEG) moving and still image-compression standards.
TL;DR: In this article, a DC-AC inverter with no inductors or transformers is presented, where the role of the magnetic devices is played by a switched-capacitor (SC) circuit, formed by two subcircuits.
Abstract: A DC-AC inverter containing no inductors or transformers is presented. The role of the magnetic devices is played by a switched-capacitor (SC) circuit, formed by two subcircuits. Each SC-subcircuit contains 15 basic cells, each one formed by one capacitor, two MOSFETs and two diodes. The sinusoidal output waveform is realized in a staircase, formed by 64 steps. To achieve each step, the inverter operates like a step-up DC-DC converter: by using a certain number of SC-cells, the input voltage is boosted to the voltage required by the step in consideration. Each step is implemented in a large number of switching cycles. In each cycle, the inverter goes through four phases; according to a designed switching sequence, some of the capacitors of the SC-cells involved in the respective step are in a charging process from line, while the others are in a discharging process to the load. The phases 2 and 4 have a regulation role only. A duty cycle control is used. A Fourier analysis evidences the clean AC output waveform. The inverter exhibits low weight, high power density, and enhanced regulation for large changes in line and load.
TL;DR: In this paper, the authors present theoretical analysis and experimental results on the dynamic behavior of a bistable microelectromechanical systems (MEMS) oscillator, demonstrate the existence of a strange attractor in the MEMS device, and perform model verification using the experimental data.
Abstract: In this paper we present theoretical analysis and experimental results on the dynamic behavior of a bistable microelectromechanical systems (MEMS) oscillator, demonstrate the existence of a strange attractor in the MEMS device, and perform model verification using the experimental data. Secure communication schemes based on synchronized chaos are also applied to the device and successfully performed in the simulation.
TL;DR: The breaking method presented in this paper is not sensitive to the order of the transmitter, which means that even in a chaotic switching scheme which uses two hyperchaotic systems, the degree of security may still be low.
Abstract: In a chaotic switching scheme, a binary message signal is scrambled by two chaotic attractors. In this paper we present examples to show how generalized chaotic synchronization (GS) can be used to break chaotic switching schemes. Since GS is a very robust phenomenon, we find that an intruder can recover the binary information signal from chaotic switching schemes without knowing both the structure and parameters of the chaotic transmitter. The breaking method presented in this paper is not sensitive to the order of the transmitter, which means that even in a chaotic switching scheme which uses two hyperchaotic systems, the degree of security may still be low. The simulation results for both low order and high order transmitters are presented.
TL;DR: In this paper, a signal flow graph (SFG) technique was used to analyze dc-dc PWM switch mode power converters operating in the continuous conduction mode (CCM).
Abstract: A systematic and unified method using the signal flow graph (SFG) technique is presented in analyzing dc-dc pulsewidth modulated (PWM) switch mode power converters (SMPC's) operating in the continuous conduction mode (CCM). Loop gains for single and multiloop systems are reviewed. The SFG of the converter is then generated from the perturbed state-space averaged (SSA) equations, and the characteristic polynomial of the system is computed. By grouping terms associated with the gain of the error amplifier as the numerator, a unique definition of system loop gain is introduced, and locations for breaking the loop are discussed. System loop gains for both voltage- and current-programming converters with either trailing- or leading-edge modulation are derived. It is shown that for a SMPC, the loop gain measured by an analog injection method is the system loop gain, which determines the stability of the converter.
TL;DR: In this paper, a general PWM modulator that realizes various control schemes with either trailing-edge or leading-edge modulation is proposed, based on that a general double-edge modulator is constructed.
Abstract: Constant-frequency pulsewidth modulation (PWM) is the most frequently used method in the control of switching converters. This paper proposes a general PWM modulator that realizes various control schemes with either trailing-edge or leading-edge modulation. Based on that a general double-edge modulator ran be constructed. The proposed modulator is applied to feedforward control of a family of converters, current-mode control with linear or nonlinear compensating slope, and a family of unity-power-factor rectifiers at continuous or discontinuous conduction mode to demonstrate its generality. Experimental and PSPICE verifications are provided.
TL;DR: The design of cellular neural networks (CNNs) which compute the outputs of filters similar to Gabor filters are described, which might eventually relieve the computational bottleneck associated with Gabor filtering image-processing algorithms.
Abstract: Gabor filters are preprocessing stages in image-processing and computer-vision applications. One drawback is that they are computationally intensive on a digital computer. This paper describes the design of cellular neural networks (CNNs) which compute the outputs of filters similar to Gabor filters. Analog VLSI implementations of these CNNs might eventually relieve the computational bottleneck associated with Gabor filtering image-processing algorithms. The CNNs compute both the real and imaginary parts of the filter outputs simultaneously, which is an important feature in applying them in algorithms utilizing the phase of the Gabor output.
TL;DR: In this article, an accurate analytical model for the evaluation of the delay and the short-circuit power dissipation of the CMOS inverter is presented. But the model does not take into account the influences of the shortcircuit current during switching, and the gate-to-drain coupling capacitance.
Abstract: This paper introduces a new, accurate analytical model for the evaluation of the delay and the short-circuit power dissipation of the CMOS inverter. Following a detailed analysis of the inverter operation, accurate expressions for the output response to an input ramp are derived. Based on this analysis improved analytical formulae for the calculation of the propagation delay and short-circuit power dissipation, are produced. Analytical expressions for all inverter operation regions and input waveform slopes are derived, which take into account the influences of the short-circuit current during switching, and the gate-to-drain coupling capacitance. The effective output transition time of the inverter is determined in order to map the real output voltage waveform to a ramp waveform for the model to be applicable in an inverter chain. The final results are in very good agreement with SPICE simulations.
TL;DR: This second of two papers studies how and when a global propagation of information is possible through a one-dimensional (1-D) Cellular Neural Network (CNN) with connections between nearest neighbors only.
Abstract: For pt.I see P. Thiran et al., ibid., vol.45, no.8, pp.777-89 (1998). This second of two papers studies how and when a global propagation of information, introduced as initial condition, is possible through a one-dimensional (1-D) Cellular Neural Network (CNN) with connections between nearest neighbors only. We will focus on circular arrays, which have the most regular structure, we will show that periodic solutions exist, and we will compute one of them analytically. We will also study their stability.
TL;DR: It is shown that a two-layer cellular neural network with constant templates is suitable for generating self-organizing patterns and, therefore, it is able to model complex phenomena.
Abstract: In this work, it is shown that a two-layer cellular neural network (CNN) with constant templates is suitable for generating self-organizing patterns and, therefore, it is able to model complex phenomena. The dynamic behavior of the single two-layer linear CNN cell is studied and the global behavior of the whole CNN is discussed. Different nonlinear phenomena are generated, including autowaves and spirals. Finally, the sensitivity with respect to parametric uncertainties and noise is investigated.
TL;DR: In this paper, analytical models for a bidirectional coupled-inductor Cuk converter operating in sliding mode are described, and the expression for the equivalent control is derived and the coordinates of the equilibrium point are obtained.
Abstract: Analytic models for a bidirectional coupled-inductor Cuk converter operating in sliding mode are described. Using a linear combination of the converter four state variable errors as a general switching surface, the expression for the equivalent control is derived and the coordinates of the equilibrium point are obtained. Particular cases of the general switching surface are subsequently analyzed in detail: (1) surfaces for ideal line regulation, (2) surfaces for ideal load regulation, and (3) surfaces for hysteretic current control. Simulation results verifying the analytical predictions are presented.
TL;DR: The N Extra Element Theorem (NEET) as mentioned in this paper is an alternative means of analysis for any transfer function of any linear system model, not restricted to electrical systems, and it can be used in practical Design-Oriented Analysis.
Abstract: The N Extra Element Theorem (NEET) is an alternative means of analysis for any transfer function of any linear system model, not restricted to electrical systems. Its principal distinction from conventional loop or node analysis is that a simpler reference system model in the absence of N designated "extra" elements is solved first, and the N extra elements are then restored via a correction factor. Parameters in the correction factor are various single injection and null double injection driving point immittances seen by the extra elements, and are all calculated upon the reference model. Thus, no calculation is performed upon a model containing any of the designated extra elements, and the final result is obtained by assembly of sequentially obtained results in a "divide and conquer" approach that is potentially easier, shorter, and which produces lower entropy forms than does the conventional approach. The NEET correction factor is a simultaneous bilinear representation of the extra elements, which can be immittances or dependent generators in any combination, and thus exposes explicitly the contribution of each extra element. An especially useful implementation of the NEET is to designate all the reactances as extra elements. The frequency response of the transfer function is then contained entirely in the NEET correction factor, which emerges directly as a ratio of polynomials in complex frequency s. The zeros as well as the poles can thus be obtained directly from the driving point resistances seen by the reactances, and it can also be determined whether any of the zeros or poles are exactly factorable. The approach throughout is to show how the NEET theorem can be useful in practical Design-Oriented Analysis, and emphasis is on the criteria by which the designer-analyst can take maximum advantage of the numerous choices of which elements to designate as "extra" and which of the many versions of the theorem to adopt.
TL;DR: In this paper, a 2D continuous-discrete Roesser's linear model is used to describe both the dynamics of the control system and the behavior of the learning process.
Abstract: This work presents a two-dimensional (2-D) system theory based iterative learning control (ILC) method for linear continuous-time multivariable systems. We demonstrate that a 2-D continuous-discrete model can be successfully applied to describe both the dynamics of the control system and the behavior of the learning process. We successfully exploited the 2-D continuous-discrete Roesser's linear model by extending the ILC technique from discrete control systems to continuous control systems. Three learning rules for ILC are derived. Necessary and sufficient conditions are given for convergence of the proposed learning rules. Compared to the learning rule suggested by Arimoto et al. (1984), our developed learning rules are less restrictive and have wider applications. The third learning rule proposed ensures the reference output trajectory can be accurately tracked after only one learning trial. Three numerical examples are used to illustrate the proposed control procedures.
TL;DR: In this article, a recursive method is proposed to obtain simultaneously all the parameters required and its convergence is studied, and an iterative method to introduce new partitions on the domain, when the error obtained is not satisfactory, is described.
Abstract: This paper deals with the approximation of smooth functions using canonical piecewise-linear functions. The developing of tools in the field of analysis and control of nonlinear systems based on this kind of functions, as well as its efficiency in the representation of electronic devices, motivates the development of useful methods to obtain accurate approximations. A recursive method is proposed to obtain simultaneously all the parameters required and its convergence is studied. In addition, an iterative method to introduce new partitions on the domain, when the error obtained is not satisfactory, is described. This method takes advantage of the partitions already found to reduce the total number of parameters that the algorithm has to handle.
TL;DR: In this article, a simplex method is proposed for finding all solutions of piecewise-linear resistive circuits, which is based on a new test for nonexistence of a solution.
Abstract: An efficient algorithm is proposed for finding all solutions of piecewise-linear resistive circuits. This algorithm is based on a new test for nonexistence of a solution to a system of piecewise-linear equations f/sub i/(x)=0(i=1.2,/spl middot//spl middot//spl middot/,n) in a super-region. Unlike the conventional sign test, which checks whether the solution surfaces of the single piecewise-linear equations exist or not in a super-region, the new test checks whether they intersect or not in the super-region. Such a test can be performed by using linear programming. It is shown that the simplex method can be performed very efficiently by exploiting the adjacency of super-regions in each step. The proposed algorithm is much more efficient than the conventional sign test algorithms and can find all solutions of large scale circuits very efficiently. Moreover, it can find all characteristic curves of piecewise-linear resistive circuits.
TL;DR: In this article, the second method of Lyapunov is utilized to establish sufficient conditions for the global asymptotic stability of the trivial solution of zero-input two-dimensional (2-D) Fornasini-Marchesini state-space digital filters which are endowed with a general class of overflow nonlinearities.
Abstract: In this paper, the second method of Lyapunov is utilized to establish sufficient conditions for the global asymptotic stability of the trivial solution of zero-input two-dimensional (2-D) Fornasini-Marchesini state-space digital filters which are endowed with a general class of overflow nonlinearities. Results for the global asymptotic stability of the null solution of the 2-D Fornasini-Marchesini second model with overflow nonlinearities are established. Several classes of Lyapunov functions are used in establishing the present results, including vector norms and the quadratic form. When the quadratic form Lyapunov functions are considered, the present results involve necessary and sufficient conditions under which positive definite matrices can be used to generate Lyapunov functions for 2-D digital filters with overflow nonlinearities.
TL;DR: This paper presents a new approach to non-Linear Modelling of Neural Network Reference LANOS-ARTICLE-1998-004 that addresses the challenge of directly simulating the dynamic response of the immune system.
Abstract: This is the first of two companion papers devoted to a deep analysis of the dynamics of information propagation in the simplest nontrivial Cellular Neural Network (CNN), which is one-dimensional and has connections between nearest neighbors only We will show that two behaviors are possible: local diffusion of information between neighboring cells and global propagation through the entire array This paper deals with local diffusion, of which we will first give an accurate definition, before computing the template parameters for which the CNN has this behavior Next we will compute the number of stable equilibria, before examining the convergence of any trajectory toward them, for three different kinds of boundary conditions: fixed Dirichlet, reflective, and periodic
TL;DR: The convergence theorem of the Gauss-Seidel method, which is an iterative technique for solving a linear algebraic equation, plays an important role in the proof of the new sufficient condition for complete stability of a nonsymmetric cellular neural network.
Abstract: This paper gives a new sufficient condition for complete stability of a nonsymmetric cellular neural network (CNN). The convergence theorem of the Gauss-Seidel method, which is an iterative technique for solving a linear algebraic equation, plays an important role in our proof. It is also shown that the existence of a stable equilibrium point does not imply complete stability of a nonsymmetric CNN.