Piecewise Linear Control Systems: A Computational Approach

✍ Scribed by Mikael K.-J. Johansson

• Publisher: Springer
• Year: 2002
• Tongue: English
• Leaves: 209
• Series: Lecture Notes in Control and Information Sciences
• Edition: 1
• 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 1
Piecewise LinearControl Systems......Page 3
Contents......Page 8
1Introduction......Page 10
Piecewise Linear Systems......Page 11
Computational Analysis of Dynamical Systems......Page 12
Philosophy of this Book......Page 15
About This Manuscript......Page 16
Model Representation......Page 18
Solution Concepts......Page 23
Uncertainty Models......Page 30
Modularity and Interconnections......Page 35
Piecewise Linear Function Representations......Page 37
Comments and References......Page 39
Equilibrium Points and the Steady-State Characteristic......Page 41
Constraint Verification and Invariance......Page 44
Detecting Attractive Sliding Modes on Cell Boundaries......Page 46
Comments and References......Page 48
Exponential Stability......Page 50
Quadratic Stability......Page 51
Conservatism of Quadratic Stability......Page 55
From Quadratic to Piecewise Quadratic......Page 57
Interlude: Describing Partition Properties......Page 60
Piecewise Quadratic Lyapunov Functions......Page 64
Analysis of Piecewise Linear Differential Inclusions......Page 70
Analysis of Systems with Attractive Sliding Modes......Page 72
Improving Computational Efficiency......Page 75
Piecewise Linear Lyapunov Functions......Page 81
A Unifying View......Page 86
Comments and References......Page 91
5. Dissipativity Analysis......Page 94
Dissipativity Analysis via Convex Optimization......Page 95
Computation of L2-induced Gain......Page 97
Estimation of Transient Energy......Page 99
Dissipative Systems with Quadratic Supply Rates......Page 100
Comments and References......Page 104
6. Controller Design......Page 105
Quadratic Stabilization of Piecewise Linear Systems......Page 106
Controller Synthesis based on Piecewise Quadratics......Page 107
Comments and References......Page 114
7. Selected Topics......Page 116
Estimation of Regions of Attraction......Page 117
Rigorous Analysis of Smooth Nonlinear Systems......Page 124
Automated Partition Refinements......Page 126
Fuzzy Logic Systems......Page 129
Comments and References......Page 135
8. Linear Hybrid Dynamical Systems......Page 138
Linear Hybrid Dynamical Systems......Page 139
Analysis Using Discontinuous Lyapunov Functions......Page 141
Stability Analysis Using Lyapunov Functionals......Page 144
Comments and References......Page 148
A. Computational Issues......Page 151
C Bibliography......Page 192