Control Systems with Actuator Saturation

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1 Control Systems with Actuator Saturation Analysis and Design Tingshu Hu Zongli Lin With 67 Figures Birkhauser Boston Basel Berlin

2 Preface xiii 1 Introduction Linear Systems with Actuator Saturation Notation, Acronyms, and Terminology 3 2 Null Controllability Continuous-Time Systems Introduction Preliminaries and Definitions General Description of Null Controllable Region Systems with Only Real Eigenvalues Systems with Complex Eigenvalues Some Remarks on the Description of C(T) Asymptotically Null Controllable Region Conclusions 35 3 Null Controllability-Discrete-Time Systems Introduction Preliminaries and Definitions General Description of Null Controllable Region Systems with Only Real Eigenvalues Systems with Complex Eigenvalues An Example Asymptotically Null Controllable Region Conclusions 53

3 4 Stabilization on Null Controllable Region - Continuous-Time Systems ' Introduction \ Domain of Attraction-Planar System under Saturated Linear Feedback Semi-Global Stabilization-Planar Systems Semi-Global Stabilization-Higher Order Systems Conclusions 83 5 Stabilization on Null Controllable Region Discrete-Time Systems Introduction Global Stabilization at Set of Equilibria- Planar Systems Global Stabilization - Planar Systems Semi-Global Stabilization - Planar Systems Semi-Global Stabilization-Higher Order Systems Conclusions Ill 6 Practical Stabilization on Null Controllable Region Introduction Problem Statement and Main Results Problem Statement Main Results: Semi-Global Practical Stabilization Proof of Main Results Properties of the Trajectories of Second Order Linear Systems Properties of the Domain of Attraction Proof of Theorem 6.2.1: Second Order Systems Proof of Theorem 6.2.1: Higher Order Systems An Example Conclusions A Proof of Lemma B Proof of Lemma Estimation of the Domain of Attraction under Saturated Linear Feedback Introduction 157

4 ix 7.2 A Measure of Set Size Some Facts about Convex Hulls _ Continuous-Time Systems under State Feedback A Set Invariance Condition Based on Circle Criterion An Improved Condition for Set Invariance The Necessary and Sufficient Condition- Single Input Systems Estimation of the Domain of Attraction Discrete-Time Systems under State Feedback Condition for Set Invariance The Necessary and Sufficient Condition- Single Input Systems Estimation of the Domain of Attraction Extension to Output Feedback Conclusions On Enlarging the Domain of Attraction Introduction Continuous-Time Systems Discrete-Time Systems Conclusions Semi-Global Stabilization with Guaranteed Regional Performance Introduction Expansion of the Domain of Attraction Semi-Globalization-Discrete-Time Systems Semi-Globalization-Continuous-Time Systems An Example Conclusions Disturbance Rejection with Stability Introduction Continuous-Time Systems Problem Statement Condition for Set Invariance 214

5 Disturbance Rejection with Guaranteed Domain of Attraction An Example Discrete-Time Systems Problem Statement Condition for Set Invariance Disturbance. Rejection with Guaranteed Domain of Attraction Conclusions On Maximizing the Convergence Rate Introduction Continuous-Time Systems Maximal Convergence Control and Maximal Invariant Ellipsoid Saturated High Gain Feedback Overall Convergence Rate Maximal Convergence Control in the Presence of Disturbances Discrete-Time Systems Conclusions Output Regulation Continuous-Time Systems Introduction Preliminaries and Problem Statement Review of Linear Output Regulation Theory Output Regulation in the Presence of Actuator Saturation The Regulatable Region State Feedback Controllers Error Feedback Controllers An Example Conclusions Output Regulation Discrete-Time Systems Introduction Preliminaries and Problem Statement Review of Linear Output Regulation Theory

6 xi Output Regulation in the Presence of Actuator Saturation The Regulatable Region State Feedback Controllers Error Feedback Controllers Conclusions Linear Systems with Non-Actuator Saturation Introduction Planar Linear Systems under State Saturation- Continuous-Time Systems System Description and Problem Statement Main Results on Global Asymptotic Stability Outline of the Proof Planar Linear Systems under State Saturation- Discrete-Time Systems System Description and Problem Statement Main Results on Global Asymptotic Stability Outline of the Proof Semi-Global Stabilization of Linear Systems Subject to Sensor Saturation Introduction Main Results An Example Conclusions 371 Bibliography 375 Index 387

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