Switched time-delay systems : stability and control /
Mahmoud, Magdi S.,
Switched time-delay systems : stability and control / Magdi S. Mahmoud. - xx, 433 pages : illustrations ; 24 cm
Includes bibliographical references and index.
Part I. Mathematical Tools : -- 1. Introduction -- 2. Mathematical Foundations -- Part II. System Stability : -- 3. Time-Delay Systems: Recent Progress -- 4. Switched Systems -- 5. Switched Time-Delay Systems -- Part III. Switched Stabilization and Control : -- 6. Three-Term Stabilization Schemes -- 7. Delay-Dependent Switched Control -- 2. Gain Analysis -- Part IV. Switched Filtering : -- 8. Delay-Dependent Switched Filtering -- 9. Switched Kalman Filtering -- Part V. Switched Decentralized Control : -- 10. Switched Decentralized Control -- Part VI. Applications : -- 11. Applications to Water-Quality Control -- 12. Applications to Mutli-Rate Control -- -- Mathematical Tools : -- Introduction -- Introduction -- Functional Differential Equations -- Piecewise Linear Dynamical Systems -- Fundamental Stability Theorems -- Lyapunov-Razumikhin Theorem -- Lyapunov-Krasovskii Theorem -- Halanay Theorem -- Outline of the Book -- Methodology -- Chapter Organization -- Mathematical Foundations -- Introduction -- Basic Mathematical Concepts -- Euclidean Space -- Norms of Vectors -- Convex Sets -- Continuous Functions -- Function Norms -- Calculus and Algebra of Matrices -- Fundamental Subspaces -- Calculus of Vector-Matrix Functions of a Scalar -- Derivatives of Vector-Matrix Products -- The Dini Theorem -- Positive Definite and Positive Semidefinite Matrices -- Trace Properties -- Partitioned Matrices -- The Matrix Inversion Lemma -- The Singular Value Decomposition -- Notes and References -- System Stability : -- Time-Delay Systems: Recent Progress -- Time Delays: Overview -- Literature Survey -- Stability Methods -- Delay-Independent Stability Tests -- Delay-Dependent Stability Tests -- Stability Results -- Stabilization Results -- Stability Approaches: Continuous Time -- Basic Models -- LMI Stability Conditions -- Newton-Leibniz Formula -- Cross-Product Terms -- Bounding Inequalities -- Descriptor System Approach -- Free-Weighting Matrices Method -- Interval Time Delays -- Improved Stability Method -- Delay-Partitioning Projection Method -- Numerical Examples -- Stability Approaches: Discrete Time -- A Discrete-Time Model -- Lyapunov Theorem -- Delay-Independent Stability -- Delay-Dependent Stability -- Descriptor Model Transformation -- Improved Stability Methods -- Simulation Examples -- Notes and References -- Switched Systems -- Introduction -- Switched Systems: Overview -- Dynamic Model -- Model and Definitions -- Arbitrary Switching -- Average Dwell Time -- Lyapunov Functions -- Converse Lyapunov Theorem -- Some Representative Examples -- Car Transmission System -- Autonomous Switched System -- Another Switched System -- Simplified Longitudinal Dynamics of an Aircraft -- L2 Gain Analysis and Synthesis -- Switched Gain Analysis -- Switched State Feedback -- Switched Static Output Feedback -- Switched Dynamic Output Feedback -- Numerical Examples -- Notes and References -- Switched Time-Delay Systems -- Introduction -- Switched Time-Delay Systems -- Multiple Lyapunov Functions -- Switched-Stability Analysis -- Illustrative Example A -- Piecewise-Affine Systems -- Continuous-Time Systems -- Solution of PWATD Continuous Systems -- Illustrative Example B -- Discrete-Time Systems -- Stability of PWA Discrete Systems -- Stability of PWATD Discrete Systems -- Synthesis of a Stabilizing State Feedback -- Illustrative Example C -- Notes and References -- Switched Stabilization and Control : -- Three-Term Stabilization Schemes -- Continuous-Time Systems -- Problem Statement -- Model Transformation -- H[infinity] Stabilization: Unknown Continuous Delay -- H[infinity] Stabilization: Time-Varying Delays -- Simulation Examples -- Discrete-Time Systems -- Introduction -- Problem Statement -- State-Feedback H[infinity] Stabilization -- Proportional-Summation-Difference (PSD) Stabilization -- Notes and References -- Delay-Dependent Switched Control -- Continuous-Time Systems -- Introduction -- Problem Statement. -- Delay-Dependent Stability -- State-Feedback Design -- H[infinity] Feedback Design -- H2 Feedback Design -- Simultaneous H -- /H[infinity] Design -- Discrete-Time Systems -- Introduction -- Problem Statement -- Delay-Dependent L -- Gain Analysis -- Switched Feedback Design -- Multi-Controller Structure -- Problem Statement -- Robust Delay-Dependent Switching Control -- Delay-Dependent Switching Control Design -- Appendix -- Notes and References -- Switched Filtering : -- Delay-Dependent Switched Filtering -- H[infinity] Filter Design -- Introduction -- Problem Formulation -- Stability and Performance Analysis -- Filter Design -- Illustrative Example A -- Filter Design for Piecewise Systems -- Problem Statement and Definitions -- Error Dynamics -- Delay-Dependent Stability -- Piecewise Lyapunov Functional -- Robust Stability -- Common Lyapunov Functional -- H[infinity] Performance -- 2 - [infinity] Performance -- H[infinity] Filter Design -- 2 - [infinity] Filter Design -- Illustrative Example B -- Illustrative Example C -- Notes and References -- Switched Kalman Filtering -- Discrete Switched Delay System -- Problem Formulation -- Switched State Estimation -- Robust Linear Filtering -- A Design Approach -- Steady-State Robust Filter -- Simulation Example -- Continuous Switched Delay System -- Problem Formulation -- Robust Linear Filtering -- A Design Approach -- Steady-State Robust Filter -- Numerical Simulation -- Notes and References -- Switched Decentralized Control : -- Switched Decentralized Control -- Interconnected Discrete-Time Systems -- Problem Statement and Preliminaries -- Decentralized -- Gain Analysis -- Switched State-Feedback Control -- Switched Dynamic Output Feedback -- Simulation Example A -- Interconnected Continuous-Time Systems -- Introduction -- Problem Statement and Preliminaries -- Delay-Dependent L -- Gain Analysis -- Switched State-Feedback Design -- Simulation Example B -- Simulation Example C -- Notes and References -- Applications : -- Applications to Water-Quality Control -- Application I: Water-Quality Control -- Motivating Example -- Delay-Dependent L2 Gain Analysis -- Switched Feedback Control -- Switched State Feedback -- Switched Static Output Feedback -- Appendix -- Proof of Theorem 11 -- Proof of Theorem 11 -- Proof of Theorem 11 -- Notes and References -- Applications to Mutli-Rate Control -- Introduction -- Problem Statement -- Dual-Rate Network Control Model -- Hybrid Control Model -- Dissipativity Analysis -- Dissipative Stability of the Nominal System -- Dissipative Synthesis of the Nominal System -- Dissipativity Stability of the Uncertain System -- Dissipative Synthesis of the Uncertain System -- Special Cases -- Numerical Simulation -- Conclusions. Part I. 1. 1.1. 1.2. 1.3. 1.4. 1.4.1. 1.4.2. 1.4.3. 1.5. 1.5.1. 1.5.2. 2. 2.1. 2.2. 2.2.1. 2.2.2. 2.2.3. 2.2.4. 2.2.5. 2.3. 2.3.1. 2.3.2. 2.3.3. 2.3.4. 2.3.5. 2.3.6. 2.3.7. 2.3.8. 2.3.9. 2.4. Part II. 3. 3.1. 3.2. 3.2.1. 3.2.2. 3.2.3. 3.2.4. 3.2.5. 3.3. 3.3.1. 3.3.2. 3.3.3. 3.3.4. 3.3.5. 3.3.6. 3.3.7. 3.3.8. 3.3.9. 3.3.10. 3.3.11. 3.4. 3.4.1. 3.4.2. 3.4.3. 3.4.4. 3.4.5. 3.4.6. 3.4.7. 3.5. 4. 4.1. 4.2. 4.2.1. 4.2.2. 4.2.3. 4.2.4. 4.2.5. 4.2.6. 4.3. 4.3.1. 4.3.2. 4.3.3. 4.3.4. 4.4. 4.4.1. 4.4.2. 4.4.3. 4.4.4. 4.4.5. 4.5. 5. 5.1. 5.2. 5.2.1. 5.2.2. 5.2.3. 5.3. 5.3.1. 5.3.2. 5.3.3. 5.3.4. 5.3.5. 5.3.6. 5.3.7. 5.3.8. 5.4. Part III. 6. 6.1. 6.1.1. 6.1.2. 6.1.3. 6.1.4. 6.1.5. 6.2. 6.2.1. 6.2.2. 6.2.3. 6.2.4. 6.3. 7. 7.1. 7.1.1. 7.1.2. 3. 7.1.4. 7.1.5. 7.1.6. 7.1.7. 2. 7.2. 7.2.1. 7.2.2. 7.2.3. 2. 7.2.4. 7.3. 7.3.1. 7.3.2. 7.3.3. 7.3.4. 7.4. Part IV. 8. 8.1. 8.1.1. 8.1.2. 8.1.3. 8.1.4. 8.1.5. 8.2. 8.2.1. 8.2.2. 8.2.3. 8.2.4. 8.2.5. 8.2.6. 8.2.7. 8.2.8. 8.2.9. 8.2.10. 8.2.11. 8.2.12. 8.3. 9. 9.1. 9.1.1. 9.1.2. 9.1.3. 9.1.4. 9.1.5. 9.1.6. 9.2. 9.2.1. 9.2.2. 9.2.3. 9.2.4. 9.2.5. 9.3. Part V. 10. 10.1. 10.1.1. 10.1.2. 2. 10.1.3. 10.1.4. 10.1.5. 10.2. 10.2.1. 10.2.2. 10.2.3. 2. 10.2.4. 10.2.5. 10.2.6. 10.3. Part VI. 11. 11.1. 11.1.1. 11.1.2. 11.1.3. 11.1.4. 11.1.5. 11.2. 11.2.1. 11.2.2. 11.2.3. 11.3. 12. 12.1. 12.2. 12.2.1. 12.2.2. 12.3. 12.3.1. 12.3.2. 12.3.3. 12.3.4. 12.4. 12.5. 12.6.
"Switched Time-Delay Systems presents an introductory, yet comprehensive, treatment of switched time-delay systems by jointly combining two fundamental attributes: the system dynamics possesses an inherent time-delay and the system operational mode undergoes switching among different modes. While each attribute has been examined individually in several texts, the integration of both attributes is quite unique and deserves special consideration. The material contained in this book is not only organized to focus on the new developments in the analysis and control methodologies for such switched time-delay systems, but it also integrates the impact of the delay factor on issues such as asymptotic/exponential stability, feedback stabilization and control design. Switched Time-Delay Systems is composed of chapters equipped with illustrative examples and relevant notes. It will be useful to engineers and researchers in the field of switched time-delay systems."--Publisher's website.
1441963936 9781441963932
Time delay systems
Switching circuits
TJ213 / .M35 2010
629.83
Switched time-delay systems : stability and control / Magdi S. Mahmoud. - xx, 433 pages : illustrations ; 24 cm
Includes bibliographical references and index.
Part I. Mathematical Tools : -- 1. Introduction -- 2. Mathematical Foundations -- Part II. System Stability : -- 3. Time-Delay Systems: Recent Progress -- 4. Switched Systems -- 5. Switched Time-Delay Systems -- Part III. Switched Stabilization and Control : -- 6. Three-Term Stabilization Schemes -- 7. Delay-Dependent Switched Control -- 2. Gain Analysis -- Part IV. Switched Filtering : -- 8. Delay-Dependent Switched Filtering -- 9. Switched Kalman Filtering -- Part V. Switched Decentralized Control : -- 10. Switched Decentralized Control -- Part VI. Applications : -- 11. Applications to Water-Quality Control -- 12. Applications to Mutli-Rate Control -- -- Mathematical Tools : -- Introduction -- Introduction -- Functional Differential Equations -- Piecewise Linear Dynamical Systems -- Fundamental Stability Theorems -- Lyapunov-Razumikhin Theorem -- Lyapunov-Krasovskii Theorem -- Halanay Theorem -- Outline of the Book -- Methodology -- Chapter Organization -- Mathematical Foundations -- Introduction -- Basic Mathematical Concepts -- Euclidean Space -- Norms of Vectors -- Convex Sets -- Continuous Functions -- Function Norms -- Calculus and Algebra of Matrices -- Fundamental Subspaces -- Calculus of Vector-Matrix Functions of a Scalar -- Derivatives of Vector-Matrix Products -- The Dini Theorem -- Positive Definite and Positive Semidefinite Matrices -- Trace Properties -- Partitioned Matrices -- The Matrix Inversion Lemma -- The Singular Value Decomposition -- Notes and References -- System Stability : -- Time-Delay Systems: Recent Progress -- Time Delays: Overview -- Literature Survey -- Stability Methods -- Delay-Independent Stability Tests -- Delay-Dependent Stability Tests -- Stability Results -- Stabilization Results -- Stability Approaches: Continuous Time -- Basic Models -- LMI Stability Conditions -- Newton-Leibniz Formula -- Cross-Product Terms -- Bounding Inequalities -- Descriptor System Approach -- Free-Weighting Matrices Method -- Interval Time Delays -- Improved Stability Method -- Delay-Partitioning Projection Method -- Numerical Examples -- Stability Approaches: Discrete Time -- A Discrete-Time Model -- Lyapunov Theorem -- Delay-Independent Stability -- Delay-Dependent Stability -- Descriptor Model Transformation -- Improved Stability Methods -- Simulation Examples -- Notes and References -- Switched Systems -- Introduction -- Switched Systems: Overview -- Dynamic Model -- Model and Definitions -- Arbitrary Switching -- Average Dwell Time -- Lyapunov Functions -- Converse Lyapunov Theorem -- Some Representative Examples -- Car Transmission System -- Autonomous Switched System -- Another Switched System -- Simplified Longitudinal Dynamics of an Aircraft -- L2 Gain Analysis and Synthesis -- Switched Gain Analysis -- Switched State Feedback -- Switched Static Output Feedback -- Switched Dynamic Output Feedback -- Numerical Examples -- Notes and References -- Switched Time-Delay Systems -- Introduction -- Switched Time-Delay Systems -- Multiple Lyapunov Functions -- Switched-Stability Analysis -- Illustrative Example A -- Piecewise-Affine Systems -- Continuous-Time Systems -- Solution of PWATD Continuous Systems -- Illustrative Example B -- Discrete-Time Systems -- Stability of PWA Discrete Systems -- Stability of PWATD Discrete Systems -- Synthesis of a Stabilizing State Feedback -- Illustrative Example C -- Notes and References -- Switched Stabilization and Control : -- Three-Term Stabilization Schemes -- Continuous-Time Systems -- Problem Statement -- Model Transformation -- H[infinity] Stabilization: Unknown Continuous Delay -- H[infinity] Stabilization: Time-Varying Delays -- Simulation Examples -- Discrete-Time Systems -- Introduction -- Problem Statement -- State-Feedback H[infinity] Stabilization -- Proportional-Summation-Difference (PSD) Stabilization -- Notes and References -- Delay-Dependent Switched Control -- Continuous-Time Systems -- Introduction -- Problem Statement. -- Delay-Dependent Stability -- State-Feedback Design -- H[infinity] Feedback Design -- H2 Feedback Design -- Simultaneous H -- /H[infinity] Design -- Discrete-Time Systems -- Introduction -- Problem Statement -- Delay-Dependent L -- Gain Analysis -- Switched Feedback Design -- Multi-Controller Structure -- Problem Statement -- Robust Delay-Dependent Switching Control -- Delay-Dependent Switching Control Design -- Appendix -- Notes and References -- Switched Filtering : -- Delay-Dependent Switched Filtering -- H[infinity] Filter Design -- Introduction -- Problem Formulation -- Stability and Performance Analysis -- Filter Design -- Illustrative Example A -- Filter Design for Piecewise Systems -- Problem Statement and Definitions -- Error Dynamics -- Delay-Dependent Stability -- Piecewise Lyapunov Functional -- Robust Stability -- Common Lyapunov Functional -- H[infinity] Performance -- 2 - [infinity] Performance -- H[infinity] Filter Design -- 2 - [infinity] Filter Design -- Illustrative Example B -- Illustrative Example C -- Notes and References -- Switched Kalman Filtering -- Discrete Switched Delay System -- Problem Formulation -- Switched State Estimation -- Robust Linear Filtering -- A Design Approach -- Steady-State Robust Filter -- Simulation Example -- Continuous Switched Delay System -- Problem Formulation -- Robust Linear Filtering -- A Design Approach -- Steady-State Robust Filter -- Numerical Simulation -- Notes and References -- Switched Decentralized Control : -- Switched Decentralized Control -- Interconnected Discrete-Time Systems -- Problem Statement and Preliminaries -- Decentralized -- Gain Analysis -- Switched State-Feedback Control -- Switched Dynamic Output Feedback -- Simulation Example A -- Interconnected Continuous-Time Systems -- Introduction -- Problem Statement and Preliminaries -- Delay-Dependent L -- Gain Analysis -- Switched State-Feedback Design -- Simulation Example B -- Simulation Example C -- Notes and References -- Applications : -- Applications to Water-Quality Control -- Application I: Water-Quality Control -- Motivating Example -- Delay-Dependent L2 Gain Analysis -- Switched Feedback Control -- Switched State Feedback -- Switched Static Output Feedback -- Appendix -- Proof of Theorem 11 -- Proof of Theorem 11 -- Proof of Theorem 11 -- Notes and References -- Applications to Mutli-Rate Control -- Introduction -- Problem Statement -- Dual-Rate Network Control Model -- Hybrid Control Model -- Dissipativity Analysis -- Dissipative Stability of the Nominal System -- Dissipative Synthesis of the Nominal System -- Dissipativity Stability of the Uncertain System -- Dissipative Synthesis of the Uncertain System -- Special Cases -- Numerical Simulation -- Conclusions. Part I. 1. 1.1. 1.2. 1.3. 1.4. 1.4.1. 1.4.2. 1.4.3. 1.5. 1.5.1. 1.5.2. 2. 2.1. 2.2. 2.2.1. 2.2.2. 2.2.3. 2.2.4. 2.2.5. 2.3. 2.3.1. 2.3.2. 2.3.3. 2.3.4. 2.3.5. 2.3.6. 2.3.7. 2.3.8. 2.3.9. 2.4. Part II. 3. 3.1. 3.2. 3.2.1. 3.2.2. 3.2.3. 3.2.4. 3.2.5. 3.3. 3.3.1. 3.3.2. 3.3.3. 3.3.4. 3.3.5. 3.3.6. 3.3.7. 3.3.8. 3.3.9. 3.3.10. 3.3.11. 3.4. 3.4.1. 3.4.2. 3.4.3. 3.4.4. 3.4.5. 3.4.6. 3.4.7. 3.5. 4. 4.1. 4.2. 4.2.1. 4.2.2. 4.2.3. 4.2.4. 4.2.5. 4.2.6. 4.3. 4.3.1. 4.3.2. 4.3.3. 4.3.4. 4.4. 4.4.1. 4.4.2. 4.4.3. 4.4.4. 4.4.5. 4.5. 5. 5.1. 5.2. 5.2.1. 5.2.2. 5.2.3. 5.3. 5.3.1. 5.3.2. 5.3.3. 5.3.4. 5.3.5. 5.3.6. 5.3.7. 5.3.8. 5.4. Part III. 6. 6.1. 6.1.1. 6.1.2. 6.1.3. 6.1.4. 6.1.5. 6.2. 6.2.1. 6.2.2. 6.2.3. 6.2.4. 6.3. 7. 7.1. 7.1.1. 7.1.2. 3. 7.1.4. 7.1.5. 7.1.6. 7.1.7. 2. 7.2. 7.2.1. 7.2.2. 7.2.3. 2. 7.2.4. 7.3. 7.3.1. 7.3.2. 7.3.3. 7.3.4. 7.4. Part IV. 8. 8.1. 8.1.1. 8.1.2. 8.1.3. 8.1.4. 8.1.5. 8.2. 8.2.1. 8.2.2. 8.2.3. 8.2.4. 8.2.5. 8.2.6. 8.2.7. 8.2.8. 8.2.9. 8.2.10. 8.2.11. 8.2.12. 8.3. 9. 9.1. 9.1.1. 9.1.2. 9.1.3. 9.1.4. 9.1.5. 9.1.6. 9.2. 9.2.1. 9.2.2. 9.2.3. 9.2.4. 9.2.5. 9.3. Part V. 10. 10.1. 10.1.1. 10.1.2. 2. 10.1.3. 10.1.4. 10.1.5. 10.2. 10.2.1. 10.2.2. 10.2.3. 2. 10.2.4. 10.2.5. 10.2.6. 10.3. Part VI. 11. 11.1. 11.1.1. 11.1.2. 11.1.3. 11.1.4. 11.1.5. 11.2. 11.2.1. 11.2.2. 11.2.3. 11.3. 12. 12.1. 12.2. 12.2.1. 12.2.2. 12.3. 12.3.1. 12.3.2. 12.3.3. 12.3.4. 12.4. 12.5. 12.6.
"Switched Time-Delay Systems presents an introductory, yet comprehensive, treatment of switched time-delay systems by jointly combining two fundamental attributes: the system dynamics possesses an inherent time-delay and the system operational mode undergoes switching among different modes. While each attribute has been examined individually in several texts, the integration of both attributes is quite unique and deserves special consideration. The material contained in this book is not only organized to focus on the new developments in the analysis and control methodologies for such switched time-delay systems, but it also integrates the impact of the delay factor on issues such as asymptotic/exponential stability, feedback stabilization and control design. Switched Time-Delay Systems is composed of chapters equipped with illustrative examples and relevant notes. It will be useful to engineers and researchers in the field of switched time-delay systems."--Publisher's website.
1441963936 9781441963932
Time delay systems
Switching circuits
TJ213 / .M35 2010
629.83