Switching in Systems and Control (Systems & Control)

✍ Scribed by Daniel Liberzon

• Publisher: Birkhäuser Boston
• Year: 2003
• Tongue: English
• Leaves: 248
• Series: Systems & Control: Foundations & Applications
• Edition: 2003
• Category: Library

✦ Synopsis

The theory of switched systems is related to the study of hybrid systems, which has gained attention from control theorists, computer scientists, and practicing engineers. This book examines switched systems from a control-theoretic perspective, focusing on stability analysis and control synthesis of systems that combine continuous dynamics with switching events. It includes a vast bibliography and a section of technical and historical notes.

✦ Table of Contents

Contents......Page 5
Preface......Page 9
I Introduction......Page 15
1.1 Classes of hybrid and switched systems.......Page 17
1.1.1 State-dependent switching......Page 19
1.1.2 Time-dependent switching......Page 20
1.1.3 Autonomous and controlled switching......Page 22
1.2.1 Ordinary differential equations......Page 23
1.2.2 Zeno behavior......Page 24
1.2.3 Sliding modes......Page 26
1.2.4 Hysteresis switching......Page 28
II Stability of Switched Systems......Page 31
2.1.1 Uniform stability concepts......Page 35
2.1.2 Common Lyapunov functions......Page 36
2.1.3 A converse Lyapunov theorem......Page 38
2.1.4 Switched linear systems......Page 40
2.1.5 A counterexample......Page 42
2.2.1 Commuting systems......Page 44
2.2.2 Nilpotent and solvable Lie algebras......Page 48
2.2.3 More general Lie algebras......Page 51
2.2.4 Discussion of Lie-algebraic stability criteria......Page 55
2.3 Systems with special structure......Page 56
2.3.1 Triangular systems......Page 57
2.3.2 Feedback systems......Page 59
2.3.3 Two-dimensional systems......Page 65
3.1 Multiple Lyapunov functions......Page 67
3.2.1 Dwell time......Page 70
3.2.2 Average dwell time......Page 72
3.3 Stability under state-dependent switching......Page 75
3.4.1 Stable convex combinations.......Page 79
3.4.2 Unstable convex combinations......Page 82
III Switching Control......Page 87
4.1.1 State-space obstacles......Page 91
4.1.2 Brockett's condition......Page 93
4.2 Nonholonomic systems......Page 95
4.2.1 The unicycle and the nonholonomic integrator......Page 97
4.3 Stabilizing an inverted pendulum......Page 103
5.1 The bang-bang principle of time-optimal control......Page 107
5.2 Hybrid output feedback......Page 110
5.3.1 Quantizers......Page 114
5.3.2 Static state quantization......Page 117
5.3.3 Dynamic state quantization......Page 122
5.3.4 Input quantization......Page 130
5.3.5 Output quantization......Page 135
5.3.6 Active probing for information......Page 138
6.1 Introductory remarks......Page 143
6.2 First pass: basic architecture......Page 145
6.3 An example: linear supervisory control......Page 148
6.4 Second pass: design objectives......Page 151
6.5.1 Multi-estimators......Page 153
6.5.2 Candidate controllers......Page 156
6.5.3 Switching logics......Page 159
6.6 Linear supervisory control revisited......Page 168
6.6.1 Finite parametric uncertainty......Page 170
6.6.2 Infinite parametric uncertainty......Page 173
6.7 Nonlinear supervisory control......Page 174
6.8 An example: a nonholonomic system with uncertainty......Page 177
IV Supplementary Material......Page 181
A.l Stability definitions......Page 183
B.6 Generators for gl(n......Page 0
A.3 Lyapunov's direct (second) method......Page 185
A.4 LaSalle's invariance principle......Page 187
A.5 Lyapunov's indirect (first) method......Page 188
A.6 Input-to-state stability......Page 189
B.l Lie algebras and their representations......Page 193
B.4 Semisimple and compact Lie algebras.......Page 195
Notes and References......Page 199
Bibliography......Page 217
Notation......Page 243
Index......Page 245