图书信息:

书  名:Stability Theory of Switched Dynamical Systems
作  者:Z.Sun and S.S.Ge
出 版 社:Springer
出版日期:2011
I S B N:978-0857292551
页  数:256

内容简介:   

  Stability issues are fundamental in the study of the many complex nonlinear dynamic behaviours within switched systems. Professors Sun and Ge present a thorough investigation of stability effects on three broad classes of switching mechanism: arbitrary switching where stability represents robustness to unpredictable and undesirable perturbation constrained switching, including random (within a known stochastic distribution), dwell-time (with a known minimum duration for each subsystem) and autonomously-generated (with a pre-assigned mechanism) switching; and designed switching in which a measurable and freely-assigned switching mechanism contributes to stability by acting as a control input. For each of these classes Stability Theory for Switched Dynamical Systems propounds: detailed stability analysis and/or design; related robustness and performance issues; connections to other well-known control problems; and many motivating and illustrative examples. Academic researchers and engineers interested in systems and control will find this book of great value in dealing with all forms of switching and it will be a useful source of complementary reading for graduate students of nonlinear systems theory.

图书目录:

1 Introduction
  1.1 Switched Dynamical Systems
  1.2 Stability and Stabilizability of Switched Systems
    1.2.1 Guaranteed Stability Under Arbitrary Switching
    1.2.2 Dwell-Time Stability
    1.2.3 Autonomous Stability Under State-Driven Switching
    1.2.4 Stochastic Stabilities Under Random Switching
    1.2.5 Stabilizing Switching Design
  1.3 Organization of the Book
  1.4 Notes and References
2 Arbitrary Switching
  2.1 Preliminaries
  2.2 Switched Nonlinear Systems
    2.2.1 Common Lyapunov Functions
    2.2.2 Converse Lyapunov Theorem
  2.3 Switched Linear Systems
    2.3.1 Relaxed System Frameworks
    2.3.2 Universal Lyapunov Functions
    2.3.3 Algebraic Criteria
    2.3.4 Extended Coordinate Transformation and Set Invariance
    2.3.5 Triangularizable Systems
  2.4 ComputationalIssues
    2.4.1 Approximating the Spectral Radius
    2.4.2 An Invariant Set Approach
  2.5 Notes and References
3 Constrained Switching
  3.1 Introduction
  3.2 Stochastic Stability
    3.2.1 Introduction
    3.2.2 Definition sand Preliminaries
    3.2.3 Stability Criteria
  3.3 Piecewise Linear Systems
    3.3.1 Introduction
    3.3.2 Piecewise Quadratic Lyapunov Function Approach
    3.3.3 Surface Lyapunov Approach
    3.3.4 Transition Analysis: A Graphic Approach
    3.3.5 Conewise Linear Systems
  3.4 Dwell-time Switching
    3.4.1 Preliminaries
    3.4.2 Homogeneous Polynomial Lyapunov Approach
    3.4.3 Combined Switching
  3.5 Notes and References
4 Designed Switching
  4.1 Preliminaries
  4.2 Stabilization via Time-Driven Switching
  4.3 Stabilization via State-Feedback Switching: The Lyapunov Approach
    4.3.1 Converse Lyapunov Theorems
    4.3.2 Nonconvexity of Lyapunov Functions
    4.3.3 Min Quadratic Lyapunov Functions: An Optimization Approach
    4.3.4 Well-Definedness of State-Feedback Stabilizing Law
  4.4 Stabilization via Mixed-Driven Switching: Aggregation and Calculation
    4.4.1 Pathwise State-Feedback Switching
    4.4.2 Computational Algorithms
  4.5 Stabilization via Mixed-Driven Switching: Robustness Analysis
    4.5.1 Distance Between Switching Signals
    4.5.2 Robustness Analysis
    4.5.3 Examples and Simulations
  4.6 Notes and References
5 Connections and Implications
  5.1 Absolute Stability for Planar Lure Systems
    5.1.1 Guaranteed Stability in the Plane
    5.1.2 Application to Absolute Stability of Planar Lure Systems
  5.2 Adaptive Control via Supervisory Switching
    5.2.1 Preliminaries
    5.2.2 Estimator-based Supervisory Switching
    5.2.3 An Example
  5.3 Stability Analysis of Fuzzy Systems via Piecewise Switching
    5.3.1 Piecewise Switched Linear Systems
    5.3.2StabilityAnalysisofT–S Fuzzy Systems
  5.4 Consensus of Multiagent Systems with Proximity Graphs
    5.4.1 Introduction
    5.4.2 A Consensus Criterion
    5.4.3 A Verifiale Criterion
  5.5 Stabilizing Design of Controllable Switched Linear Systems
    5.5.1 Problem Formulation
    5.5.2 Multilinear Feedback Design
  5.6 Notes and References
References
Index


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