Piecewise linear control systems: a computational approach

✍ Scribed by Johansson M.

• Publisher: Springer
• Year: 2003
• Tongue: English
• Leaves: 210
• Series: Lecture Notes in Control and Information Sciences 0284
• Category: Library

✦ Synopsis

This book presents a computational approach to the analysis of nonlinear and uncertain systems. The main focus is systems with piecewise linear dynamics. The class of piecewise linear systems examined has nonlinear, possibly discontinuous dynamics, and allows switching rules that incorporate memory and logic. These systems may exhibit astonishingly complex behaviors. Some aspects of the successful theory of linear systems and quadratic criteria are extended here to piecewise linear systems and piecewise quadratic criteria. The book also describes numerical procedures for assessing stability, computing induced gains, and solving optimal control problems for piecewise linear systems. These developments enable researchers to analyze a large and practically important class of control systems that are not easily dealt with when using other techniques.

✦ Table of Contents

Lecture Notesin Control and Information Sciences......Page 2
Piecewise LinearControl Systems......Page 4
Contents......Page 9
1 Introduction......Page 11
Piecewise Linear Systems......Page 12
Computational Analysis of Dynamical Systems......Page 13
Philosophy of this Book......Page 16
About This Manuscript......Page 17
Model Representation......Page 19
Solution Concepts......Page 24
Uncertainty Models......Page 31
Modularity and Interconnections......Page 36
Piecewise Linear Function Representations......Page 38
Comments and References......Page 40
Equilibrium Points and the Steady-State Characteristic......Page 42
Constraint Verification and Invariance......Page 45
Detecting Attractive Sliding Modes on Cell Boundaries......Page 47
Comments and References......Page 49
Exponential Stability......Page 51
Quadratic Stability......Page 52
Conservatism of Quadratic Stability......Page 56
From Quadratic to Piecewise Quadratic......Page 58
Interlude: Describing Partition Properties......Page 61
Piecewise Quadratic Lyapunov Functions......Page 65
Analysis of Piecewise Linear Differential Inclusions......Page 71
Analysis of Systems with Attractive Sliding Modes......Page 73
Improving Computational Efficiency......Page 76
Piecewise Linear Lyapunov Functions......Page 82
A Unifying View......Page 87
Comments and References......Page 92
5. Dissipativity Analysis......Page 95
Dissipativity Analysis via Convex Optimization......Page 96
Computation of L2-induced Gain......Page 98
Estimation of Transient Energy......Page 100
Dissipative Systems with Quadratic Supply Rates......Page 101
Comments and References......Page 105
6. Controller Design......Page 106
Quadratic Stabilization of Piecewise Linear Systems......Page 107
Controller Synthesis based on Piecewise Quadratics......Page 108
Comments and References......Page 115
7. Selected Topics......Page 117
Estimation of Regions of Attraction......Page 118
Rigorous Analysis of Smooth Nonlinear Systems......Page 125
Automated Partition Refinements......Page 127
Fuzzy Logic Systems......Page 130
Comments and References......Page 136
8. Linear Hybrid Dynamical Systems......Page 139
Linear Hybrid Dynamical Systems......Page 140
Analysis Using Discontinuous Lyapunov Functions......Page 142
Stability Analysis Using Lyapunov Functionals......Page 145
Comments and References......Page 149
A. Computational Issues......Page 152
C Bibliography......Page 193