There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Preface 1. Introduction Overview A Brief History of LMIs in Control Theory Notes on the Style of the Book Origin of the Book 2. Some Standard Problems Involving LMIs. Linear Matrix Inequalities Some Standard Problems Ellipsoid Algorithm Interior-Point Methods Strict and Nonstrict LMIs Miscellaneous Results on Matrix Inequalities Some LMI Problems with Analytic Solutions 3. Some Matrix Problems. Minimizing Condition Number by Scaling Minimizing Condition Number of a Positive-Definite Matrix Minimizing Norm by Scaling Rescaling a Matrix Positive-Definite Matrix Completion Problems Quadratic Approximation of a Polytopic Norm Ellipsoidal Approximation 4. Linear Differential Inclusions. Differential Inclusions Some Specific LDIs Nonlinear System Analysis via LDIs 5. Analysis of LDIs: State Properties. Quadratic Stability Invariant Ellipsoids 6. Analysis of LDIs: Input/Output Properties. Input-to-State Properties State-to-Output Properties Input-to-Output Properties 7. State-Feedback Synthesis for LDIs. Static State-Feedback Controllers State Properties Input-to-State Properties State-to-Output Properties Input-to-Output Properties Observer-Based Controllers for Nonlinear Systems 8. Lure and Multiplier Methods. Analysis of Lure Systems Integral Quadratic Constraints Multipliers for Systems with Unknown Parameters 9. Systems with Multiplicative Noise. Analysis of Systems with Multiplicative Noise State-Feedback Synthesis 10. Miscellaneous Problems. Optimization over an Affine Family of Linear Systems Analysis of Systems with LTI Perturbations Positive Orthant Stabilizability Linear Systems with Delays Interpolation Problems The Inverse Problem of Optimal Control System Realization Problems Multi-Criterion LQG Nonconvex Multi-Criterion Quadratic Problems Notation List of Acronyms Bibliography Index.

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Linear Matrix Inequalities in System and Control Theory

Forecasting with artificial neural networks: the state of the art

Being a motion on a discontinuity set of a dynamic system, sliding mode is used to keep accurately a given constraint and features theoretically-infinite-frequency switching. Standard sliding modes provide for finite-time convergence, precise keeping of the constraint and robustness with respect to internal and external disturbances. Yet the relative degree of the constraint has to be 1 and a dangerous chattering effect is possible. Higher-order sliding modes preserve or generalize the main properties of the standard sliding mode and remove the above restrictions. r-Sliding mode realization provides for up to the rth order of sliding precision with respect to the sampling interval compared with the first order of the standard sliding mode. Such controllers require higher-order real-time derivatives of the outputs to be available. The lacking information is achieved by means of proposed arbitrary-order robust exact differentiators with finite-time convergence. These differentiators feature optimal asymptot...

/pdf/higher-order-sliding-modes-differentiation-and-output-438zdzb0ld.pdf

Higher-order sliding modes, differentiation and output-feedback control

关于Semigroups of Linear Operators and Applications to Partial Differential Equations的两个注解

We consider a single-input single-output nonlinear system which has a well defined normal form with asymptotically stable zero dynamics. We study the design of a robust output feedback controller, that incorporates a linear servo compensator, to achieve asymptotic tracking and disturbance rejection. We determine the least amount of precise information about the plant that is needed to design the controller. Such design will be robust to plant parameters and uncertainties which are not used in the design calculations. We also study the robustness of the design to errors in determining the linear servo compensator. Such errors could arise from approximating a general continuous nonlinear function by a polynomial one, or from errors in determining the frequencies of the exogenous signals. We give regional as well as semiglobal results.

On the design of robust servomechanisms for minimum phase nonlinear systems

The theory of high-gain observers has been developed for about twenty years. This paper is a brief introduction to high-gain observers in nonlinear feedback control, with emphasis on the peaking phenomenon and the role of control saturation in dealing with it. The paper surveys recent results on the nonlinear separation principle, conditional servo compensators, extended high-gain observers, performance in the presence of measurement noise, sampled-data control, and experimental testbeds.

High-gain observers in nonlinear feedback control

Feedback control of linear time-invariant singularly perturbed systems of the form x=A/sub 11/x+A/sub 12/z+B/sub 1/u, epsilon z=A/sub 21/x+A/sub 22/z+B/sub 2/u,y=C/sub 1/x+C/sub 2/z Eu, where A/sub 22/ may be singular, is discussed. It is shown that, under stabilizability-detectability assumptions on the slow and fast models, the theory of feedback control of singularly perturbed systems can be extended to the case of singular A/sub 22/. Both state and output feedback results are given. In particular, a parameterization of all compensators that stabilize the system while preserving its two-time-scale structure is given. It is shown that any two-frequency-scale stabilizing compensator can be asymptotically approximated by a compensator designed via a sequential procedure. In this procedure, a fast (high-frequency) compensator is designed first to stabilize the fast model of the system. Then, a strictly proper slow (low-frequency) compensator is designed to stabilize a modified slow model. The overall compensator is taken as a parallel or cascade connection of the slow and fast compensators. The sequential procedure is applied to the design of high-gain feedback compensators for a class of multivariable plants. >

http://ieeexplore.ieee.org/iel4/9/1464/00035275.pdf

Feedback control of nonstandard singularly perturbed systems

High-gain observers play an important role in the design of feedback control for nonlinear systems This article overviews the essentials of this technique, starting with motivating examples that illustrate the main features of highgain observers, with emphasis on the peaking phenomenon and the role of control saturation in dealing with it The observer design for single-output and multi-output systems is presented along with the use of the observer in feedback control A nonlinear separation principle is discussed, and the use of an extended high-gain observer as a disturbance estimator is covered The most serious challenge in implementing high-gain observers is the effect of measurement noise, which is covered next The article ends by presenting an experimental application of the extended high-gain observer to speed control of a permanent magnet synchronous motor (PMSM)

High-Gain Observers in Feedback Control: Application to Permanent Magnet Synchronous Motors

Linear quadratic regulators for singularly perturbed difference equations are considered. Asymptotic behaviour of the optimal solution as the perturbation parameter tends to zero is studied. The composite feedback control strategy of continuous-time singularly perturbed systems is extended to the new problem.

Hassan K. Khalil

Papers

On the design of robust servomechanisms for minimum phase nonlinear systems

High-gain observers in nonlinear feedback control

Feedback control of nonstandard singularly perturbed systems

High-Gain Observers in Feedback Control: Application to Permanent Magnet Synchronous Motors

Infinite-time regulators for singularly perturbed difference equations.