Differential Linear Matrix Inequalities: In Sampled-Data Systems Filtering and Control

Description

This book is entirely devoted to sampled-data control systems analysis and design from a new point of view, which has at its core a mathematical tool named Differential Linear Matrix Inequality - DLMI, a natural generalization of Linear Matrix Inequality - LMI, that had an important and deep impact on systems and control theory almost thirty years ago. It lasts until now. It is shown that the DLMI is well adapted to deal with the important class of sampled-data control systems in both theoretical and numerical contexts. All design conditions are expressed by convex programming problems, including when robustness against parameter uncertainty is assessed and imposed through state feedback control. Special attention is given to filter, dynamic output feedback and model predictive control design, as well as nonlinear systems of Lur’e class and Markov jump linear systems.  The subject is treated with mathematical rigor, at the same time, trying to keep the reading agreeable and fruitful for colleagues and students. To this respect, the book contains together with the theoretical developments, many solved illustrative examples and the formulation of some open problems that could be faced and hopefully solved by interested readers. Preface Brief Scope and Description Contents About the Author 1 Preliminaries 1.1 Introduction 1.2 Linear Matrix Inequality 1.3 Differential Linear Matrix Inequality 1.3.1 A Fundamental Lemma on Stabilizability 1.4 Chapters' Outline 1.5 Notation 1.6 Bibliography Notes 2 Differential Linear Matrix Inequalities 2.1 Introduction 2.2 Lyapunov Differential Inequality 2.3 Riccati Differential Inequality 2.4 Numerical Solution 2.5 Bibliography Notes 3 Sampled-Data Control Systems 3.1 Introduction 3.2 Sampled-Data Systems 3.3 Stability 3.4 Performance 3.4.1 Equivalent System 3.4.2 H2 Performance Analysis and Design 3.4.3 H∞ Performance Analysis and Design 3.5 Bibliography Notes 4 H2 Filtering and Control 4.1 Introduction 4.2 H2 Performance Analysis 4.2.1 Hybrid Linear Systems 4.3 State Feedback Design 4.4 Filter Design 4.5 Dynamic Output Feedback Design 4.6 Bibliography Notes 5 H∞ Filtering and Control 5.1 Introduction 5.2 H∞ Performance Analysis 5.3 State Feedback Design 5.4 Filter Design 5.5 Dynamic Output Feedback Design 5.6 Bibliography Notes 6 Markov Jump Linear Systems 6.1 Introduction 6.2 MJLS Model 6.3 H2 Performance Analysis and Design 6.3.1 State Feedback Design 6.3.2 Filter Design 6.3.3 Dynamic Output Feedback Design 6.4 H∞ Performance Analysis and Design 6.4.1 State Feedback Design 6.4.2 Filter Design 6.4.3 Dynamic Output Feedback Design 6.5 Bibliography Notes 7 Nonlinear Systems Control 7.1 Introduction 7.2 Sampled-Data Lur'e Systems 7.3 Bibliography Notes 8 Model Predictive Control 8.1 Introduction 8.2 Model Predictive Control 8.3 Nonlinear Sampled-Data Control 8.3.1 Unconstrained Control 8.3.2 Constrained Control 8.4 Sampled-Data MPC 8.5 Bibliography Notes 9 Numerical Experiments 9.1 Introduction 9.2 Inverted Pendulum 9.2.1 State Feedback Control 9.2.2 Dynamic Output Feedback Control 9.2.3 Model Predictive Control 9.3 An Economic System 9.3.1 State Feedback Control 9.3.2 Dynamic Output Feedback Control 9.4 Bibliography Notes References Index