Showing papers by "Anthony N. Michel published in 1999"

Robust stabilizing control laws for a class of second-order switched systems

Abstract: For a class of second-order switched systems consisting of two linear time-invariant (LTI) subsystems, we show that the so-called conic switching law proposed previously by the present authors is robust, not only in the sense that the control law is flexible (to be explained further), but also in the sense that the Lyapunov stability (resp. Lagrange stability) properties of the switched system are preserved in the presence of certain kinds of vanishing perturbations (resp., nonvanishing perturbations). The analysis is possible since the conic switching laws always possess certain kinds of "quasiperiodic switching operations". We also propose for a class of nonlinear second-order switched systems with time-invariant subsystems a switching control law which locally exponentially stabilizes the entire nonlinear switched system, provided that the conic switching law exponentially stabilizes the linearized switched systems (consisting of the linearization of each nonlinear subsystem). This switched control law is robust in the sense mentioned above.

Stability analysis for a class of nonlinear switched systems

Abstract: In the present paper, we study several qualitative properties of a class of nonlinear switched systems under certain switching laws. First, we show that if all the subsystems are linear time-invariant and the system matrices are commutative componentwise and stable, then the entire switched system is globally exponentially stable under arbitrary switching laws. Next, we study the above linear switched systems with certain nonlinear perturbations, which can be either vanishing or nonvanishing. Under reasonable assumptions, global exponential stability is established for these systems. We further study the stability and instability properties, under certain switching laws, for switched systems with commutative subsystem matrices that may be unstable. Results for both continuous-time and discrete-time cases are presented.

Robustness analysis of a class of discrete-time recurrent neural networks under perturbations

Abstract: A robustness analysis is conducted for a large class of discrete-time recurrent neural networks for associative memories under perturbations of system parameters. The present paper aims to give an answer to the following question. Given a discrete-time neural network with specified stable memories (specified asymptotically stable equilibria), under what conditions will a perturbed model of the discrete-time neural network possess stable memories that are close (in distance) to the stable memories of the unperturbed discrete-time neural network model? Robustness stability results for perturbed discrete-time neural network models are established and conditions are obtained for the existence of asymptotically stable equilibria of the perturbed discrete-time neural network models which are near the asymptotically stable equilibria of the original unperturbed neural networks. In the present results, quantitative estimates (explicit estimates of bounds) are given for the distance between the corresponding equilibrium points of the unperturbed and perturbed discrete-time neural network models considered herein.

Quantized sampled-data feedback stabilization for linear and nonlinear control systems

Abstract: We propose a new control strategy which uses quantized sampled data of the states (i.e., incomplete knowledge of the states) with quantizer sensitivities that vary (i.e., depend on the values of the states) as the system evolves. The resulting closed-loop system may be viewed as a hybrid system that incorporates discrete event driven data that act upon the continuous-time component (the plant) of the entire system. For linear systems that are stabilizable by linear time-invariant feedback, we propose a quantized sampled-data control policy which globally and exponentially stabilizes the systems. Furthermore, we show that by appropriately choosing the saturation levels, the proposed control policy is robust in the presence of certain classes of perturbations. We also study the local stabilization and robustness problems for nonlinear control systems via linearization.

Robustness analysis of digital feedback control systems with time-varying sampling periods

Abstract: We study robustness properties of a class of digital feedback control systems with time-varying sampling periods consisting of an interconnection of a continuous-time nonlinear plant (described by systems of first-order ordinary differential equations), a nonlinear digital controller (described by systems of first-order ordinary difference equations), and appropriate interface elements between the plant and controller (A/D and D/A converters). For such systems, we establish results for exponential stability of an equilibrium (in the Lyapunov sense) in the presence of vanishing perturbations and for the boundedness of solutions (i.e., Lagrange stability) under the influence of non-vanishing perturbations. We apply these results to the study of quantization effects.