时滞系统的鲁棒控制和稳定性分析
2010-1
科学出版社
Min Wu，Yong He，JinHua She 主编
336
A system is said to have a delay when the rate of variation in the system state depends on past states. Such a system is called a time-delay system.Delays appear frequently in real-world engineering systems. They are often a source of instability and poor performance， and greatly increase the difficulty of stability analysis and control design. So， many researchers in the field of control theory and engineering study the robust control of time-delay systems.The study of such systems has been very active for the last 20 years; and new developments， such as fixed model transformations based on the Newton-Leibnitz formula and parameterized model transformations， are continually appearing. Although these methods are a great improvement over previous ones， they still have their limitations. We recently devised a method called the free-weighting-matrix （FWM）approach for the stability analysis and control synthesis of various classes of time-delay systems; and we obtained a series of not so conservative delay-dependent stability criteria and controller design methods. This book is based primarily on our recent research. It focuses on the stability analysis and robust control of various time-delay systems， and includes such topics as stability analysis， stabilization， control design， and filtering. The main method employed is the FWM approach. The effectiveness of this method and its advantages over other existing ones are proven theoretically and illustrated by means of various examples. The book will give readers an overview of the latest advances in this active research area and equip them with a state-of- the-art method for studying time-delay systems. This book is a useful reference for control theorists and mathematicians working with time-delay systems， engineering designing controllers for plants or systems with delays， and for graduate students interested in robust control theory and/or its application to time-delay systems.
Stability Analysis and Robust Control of Time-Delay Systems focuses on essential aspects of this field, including the stability analysis,stabilization, control design, and filtering of various time-delay systems:Primarily based on the most recent research, this monograph presents all the above areas using a free-weighting matrix approach first developed by the authors. The effectiveness of this method and its advantages over other existing ones are proven theoretically and illustrated by means of various examples. The book will give readers an overview of the latest advances in this active research area and equip them with a pioneering method for studying time-delay systems.It will be of significant interest to researchers and practitioners engaged in automatic control engineering.
Prof. Min Wu, senior member of the IEEE, works at the Central South University, China.
1.Introduction 1.1 Review of Stability Analysis for Time-Delay Systems 1.2 Introduction to FWMs 1.3 Outline of This Book References2.Preliminaries 2.1 Lyapunov Stability and Basic Theorems 2.1.1 Types of Stability 2.1.2 Lyapunov Stability Theorems 2.2 Stability of Time-Delay Systems 2.2.1 Stability-Related Topics 2.2.2 Lyapunov-Krasovskii Stability Theorem 2.2.3 Razumikhin Stability Theorem 2.3 H∞ Norm 2.3.1 Norm 2.3.2 H∞ Norm 2.4 H∞ Control 2.5 LMI Method 2.5.1 Common Specifications of LMIs 2.5.2 Standard LMI Problems 2.6 Lemmas 2.7 Conclusion References3.Stability of Systems with Time-Varying Delay 3.1 Problem Formulation 3.2 Stability of Nominal System 3.2.1 Replacing the Term x(t) 3.2.2 Retaining the Term x(t) 3.2.3 Equivalence Analysis 3.3 Stability of Systems with Time-Varying Structured Uncertainties 3.3.1 Robust Stability Analysis 3.3.2 Numerical Example 3.4 Stability of Systems with Polytopic-Type Uncertainties 3.4.1 Robust Stability Analysis 3.4.2 Numerical Example 3.5 IFWM Approach 3.5.1 Retaining Useful Terms 3.5.2 Further Investigation 3.5.3 Numerical Examples 3.6 Conclusion References4.Stability of Systems with Multiple Delays 4.1 Problem Formulation 4.2 Two Delays 4.2.1 Nominal Systems 4.2.2 Equivalence Analysis 4.2.3 Systems with Time-Varying Structured Uncertainties 4.2.4 Numerical Examples 4.3 Multiple Delays 4.4 Conclusion References5.Stability of Neutral Systems 5.1 Neutral Systems with Time-Varying Discrete Delay 5.1.1 Problem Formulation 5.1.2 Nominal Systems 5.1.3 Systems with Time-Varying Structured Uncertainties 5.1.4 Numerical Example 5.2 Neutral Systems with Identical Discrete and Neutral Delays 5.2.1 FWM Approach 5.2.2 FWM Approach in Combination with Parameterized Model Transformation 5.2.3 FWM Approach in Combination with Augmented Lyapunov-Krasovskii Functional 5.2.4 Numerical Examples 5.3 Neutral Systems with Different Discrete and Neutral Delays 5.3.1 Nominal Systems 5.3.2 Equivalence Analysis 5.3.3 Systems with Time-Varying Structured Uncertainties 5.3.4 Numerical Example 5.4 Conclusion References6.Stabilization of Systems with Time-Varying Delay 6.1 Problem Formulation 6.2 Iterative Nonlinear Minimization Algorithm 6.3 Parameter-Tuning Method 6.4 Completely LMI-Based Design Method 6.5 Numerical Example 6.6 Conclusion References7.Stability and Stabilization of Discrete-Time Systems with Time-Varying Delay 7.1 Problem Formulation 7.2 Stability Analysis 7.3 Controller Design 7.3.1 SOF Controller 7.3.2 DOF Controller 7.4 Numerical Examples 7.5 Conclusion References8.H∞ Control Design for Systems with Time-Varying Delay 8.1 Problem Formulation 8.2 BRL 8.3 Design of State-Feedback H∞ Controller 8.4 Numerical Examples 8.5 Conclusion References9.H∞ Filter Design for Systems with Time-Varying Delay 9.1 H∞ Filter Design for Continuous-Time Systems 9.1.1 Problem Formulation 9.1.2 H∞ Performance Analysis 9.1.3 Design of H∞ Filter 9.1.4 Numerical Examples 9.2 H∞ Filter Design for Discrete-Time Systems 9.2.1 Problem Formulation 9.2.2 H∞ Performance Analysis 9.2.3 Design of H∞ Filter 9.2.4 Numerical Example 9.3 Conclusion References10.Stability of Neural Networks with Time-Varying Delay. 10.1 Stability of Neural Networks with Multiple Delays 10.1.1 Problem Formulation 10.1.2 Stability Criteria 10.1.3 Numerical Examples 10.2 Stability of Neural Networks with Interval Delay 10.2.1 Problem Formulation 10.2.2 Stability Criteria 10.2.3 Numerical Examples 10.3 Exponential Stability of Continuous-Time Neural Networks 10.3.1 Problem Formulation 10.3.2 Stability Criteria Derived by FWM Approach 10.3.3 Stability Criteria Derived by IFWM Approach 10.3.4 Numerical Examples 10.4 Exponential Stability of Discrete-Time Recurrent Neural Networks 10.4.1 Problem Formulation 10.4.2 Stability Criterion Derived by IFWM Approach 10.4.3 Numerical Examples 10.5 Conclusion References11.Stability of T-S Fuzzy Systems with Time-Varying Delay 11.1 Problem Formulation 11.2 Stability Analysis 11.3 Numerical Examples 11.4 Conclusion References12.Stability and Stabilization of NCSs 12.1 Modeling of NCSs with Network-Induced Delay 12.2 Stability Analysis 12.3 Controller Design 12.4 Numerical Examples 12.5 Conclusion References13.Stability of Stochastic Systems with Time-Varying Delay 13.1 Robust Stability of Uncertain Stochastic Systems 13.1.1 Problem Formulation 13.1.2 Robust Stability Analysis 13.1.3 Numerical Example 13.2 Exponential Stability of Stochastic Markovian Jump Systems with Nonlinearities 13.2.1 Problem Formulation 13.2.2 Exponential-Stability Analysis 13.2.3 Numerical Example 13.3 Conclusion References14.Stability of Nonlinear Time-Delay Systems 14.1 Absolute Stability of Nonlinear Systems with Delay and Multiple Nonlinearities 14.1.1 Problem Formulation 14.1.2 Nominal Systems 14.1.3 Systems with Time-Varying Structured Uncertainties 14.1.4 Numerical Examples 14.2 Absolute Stability of Nonlinear Systems with Time-Varying Delay 14.2.1 Problem Formulation 14.2.2 Nominal Systems 14.2.3 Systems with Time-Varying Structured Uncertainties 14.2.4 Numerical Example 14.3 Stability of Systems with Interval Delay and Nonlinear Perturbations 14.3.1 Problem Formulation 14.3.2 Stability Results 14.3.3 Further Results Obtained with Augmented Lyapunov-Krasovskii Functional 14.3.4 Numerical Examples 14.4 Conclusion ReferencesIndex
In many physical and biological phenomena， the rate of variation in the sys-tem state depends on past states. This characteristic is called a delay or a time delay， and a system with a time delay is called a time-delay system. Time-delay phenomena were first discovered in biological systems and were later found in many engineering systems， such as mechanical transmissions， fluid transmissions， metallurgical processes， and networked control systems. They are often a source of instability and poor control performance. Time delay systems have attracted the attention of many researchers [1-3] because of their importance and widespread occurrence. Basic theories describing such systems were established in the 1950s and 1960s; they covered topics such as the existence and uniqueness of solutions to dynamic equations， stability theory for trivial solutions， etc. That work laid the foundation for the later analysis and design of time-delay systems. The robust control of time-delay systems has been a very active field for the last 20 years and has spawned many branches， for example， stability analysis， stabilization design， H∞control， passive and dissipative control，reliable control， guaranteed-cost control， H∞filtering， Kalman filtering， and stochastic control. Regardless of the branch， stability is the foundation. So，important developments in the field of time-delay systems that explore new directions have generally been launched from a consideration of stability as the starting point. This chapter reviews methods of studying the stability of time-delay systems and points out their limitations， and then goes on to describe a new method called the free-weighting-matrix （FWM） approach.
