Analysis and control of nonlinear systems with stationary sets : time-domain and frequency-domain methods /
This book presents the analysis as well as methods based on the global properties of systems with stationary sets in a unified time-domain and frequency-domain framework. The focus is on multi-input and multi-output systems, compared to previous publications which considered only single-input and si...
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| Other Authors: | |
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| Format: | Electronic eBook |
| Language: | English |
| Published: |
Hackensack, N.J. :
World Scientific,
©2009.
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| Subjects: | |
| Online Access: | CONNECT |
Table of Contents:
- Cover
- Contents
- Preface
- Notation and Symbols
- 1. Linear Systems and Linear Matrix Inequalities
- 1.1 Controllability and observability of linear systems
- 1.1.1 Controllability and observability
- 1.1.2 Stabilizability and detectability
- 1.2 Algebraic Lyapunov equations and Lyapunov inequalities
- 1.2.1 Continuous-time algebraic Lyapunov equations
- 1.2.2 Continuous-time Lyapunov inequalities
- 1.2.3 Discrete-time algebraic Lyapunov equations and inequalities
- 1.3 Formulation related to linear matrix inequalities
- 1.3.1 Schur complements
- 1.3.2 Projection lemma
- 1.4 The S-procedure
- 1.4.1 The S-procedure for nonstrict inequalities
- 1.4.2 The S-procedure for strict inequalities
- 1.5 Kalman-Yakubovi183;c-Popov (KYP) lemma and its general- ized forms
- 1.6 Notes and references
- 2. LMI Approach to H1 Control
- 2.1 L1 norm and H1 norm of the systems
- 2.1.1 L1 and H1 spaces
- 2.1.2 Computing L1 and H1 norms
- 2.2 Linear fractional transformations
- 2.3 Redheffer star product
- 2.4 Algebraic Riccati equations
- 2.4.1 Solvability conditions for Riccati equations
- 2.4.2 Discrete Riccati equation
- 2.5 Bounded real lemma
- 2.6 Small gain theorem
- 2.7 LMI approach to H1 control
- 2.7.1 Continuous-time H1 control
- 2.7.2 Discrete-time H1 control
- 2.8 Notes and references
- 3. Analysis and Control of Positive Real Systems
- 3.1 Positive real systems
- 3.2 Positive real lemma
- 3.3 LMI approach to control of SPR
- 3.4 Relationship between SPR control and SBR control
- 3.5 Multiplier design for SPR
- 3.6 Notes and references
- 4. Absolute Stability and Dichotomy of Lur'e Systems
- 4.1 Circle criterion of SISO Lur'e systems
- 4.2 Popov criterion of SISO Lur'e systems
- 4.3 Aizerman and Kalman conjectures
- 4.4 MIMO Lur'e systems
- 4.5 Dichotomy of Lur'e systems
- 4.6 Bounded derivative conditions
- 4.7 Notes and references
- 5. Pendulum-like Feedback Systems
- 5.1 Several examples
- 5.2 Pendulum-like feedback systems
- 5.2.1 The first canonical form of pendulum-like feedback system
- 5.2.2 The second canonical form of pendulum-like feed- back system
- 5.2.3 The relationship between the 175;rst and the second forms of pendulum-like feedback systems
- 5.3 Dichotomy of pendulum-like feedback systems
- 5.3.1 Dichotomy of the second form of autonomous pendulum-like feedback systems
- 5.3.2 Dichotomy of the first form of pendulum-like feed- back systems
- 5.4 Gradient-like property of pendulum-like feedback systems
- 5.4.1 Gradient-like property of the second form of pendulum-like feedback systems
- 5.4.2 Gradient-like property of the first form of pendulum-like feedback systems
- 5.5 Lagrange stability of pendulum-like feedback systems
- 5.6 Bakaev stability of pendulum-like feedback systems
- 5.7 Notes and references
- 6. Controller Design for a Class of Pendulum-like Systems
- 6.1 Controller design with dichotomy or gradient-like property
- 6.1.1 Controller design with dichotomy
- 6.1.2 Controller design with gradient-like property
- 6.2 Controller design with Lagrange stability
- 6.3 Notes and references
- 7. Controller Designs for Systems with Input Nonlinearities
- 7.1 Lagrange stabilizing for systems with input nonlinearities
- 7.2 Bakaev stabilizing for systems with input nonlinearities
- 7.3 Control for systems with input nonlinearities guaranteeing di.
