本书针对时滞系统的时滞相关鲁棒控制问题，提出一种全新的自由权矩阵方法。通过分析目前国际上处理时滞相关条件最广泛有效的确定模型变换方法及其局限性，引入自由权矩阵表示牛顿－莱布尼茨公式中各项的相互关系，建立了时变时滞系统的时滞相关鲁棒稳定性条件，并应用自由权矩阵方法，对多时滞系统和中立型时滞系统的稳定性问题进行了研究。在此基础上，将稳定性分析的结果应用于时滞相关鲁棒镇定设计。同时，将自由权矩阵的思想推广到离散时滞系统，获得了相应的时滞相关稳定性和镇定设计结果。更进一步，利用自由权矩阵方法，讨论了时滞系统的性能分析和控制器设计方法。最后，将自由权矩阵方法应用到具有非线性扇形输入的Lurie控制系统。

1.Introduction

 1.1 Review of Stability Analysis for Time-Delay Systems

 1.2 Introduction to FWMs

 1.3 Outline of This Book

 References

2.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

 References

3.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

 References

4.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

 References

5.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

 References

6.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

 References

7.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

 References

8.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

 References

9.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

 References

10.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

 References

11.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

  References

12.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

 References

13.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

 References

14.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

 References

Index