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E-raamat: Analysis and Design of Markov Jump Systems with Complex Transition Probabilities

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Analysis and Design of Markov Jump Systems with Complex Transition ProbabilitiesSuurem pilt
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The book addresses the control issues such as stability analysis, control synthesis and filter design of Markov jump systems with the above three types of TPs, and thus is mainly divided into three parts. Part I studies the Markov jump systems with partially unknown TPs. Different methodologies with different conservatism for the basic stability and stabilization problems are developed and compared. Then the problems of state estimation, the control of systems with time-varying delays, the case involved with both partially unknown TPs and uncertain TPs in a composite way are also tackled. Part II deals with the Markov jump systems with piecewise homogeneous TPs. Methodologies that can effectively handle control problems in the scenario are developed, including the one coping with the asynchronous switching phenomenon between the currently activated system mode and the controller/filter to be designed. Part III focuses on the Markov jump systems with memory TPs. The concept of s-mean square stability is proposed such that the stability problem can be solved via a finite number of conditions. The systems involved with nonlinear dynamics (described via the Takagi-Sugeno fuzzy model) are also investigated. Numerical and practical examples are given to verify the effectiveness of the obtained theoretical results. Finally, some perspectives and future works are presented to conclude the book.

Arvustused

This book collects some of the authors previous results on Markov jump systems (MJSs) subject to complex transition probabilities (TPs) as well as the original developments on the stability analysis of MJSs. This book can be used in undergraduate and graduate study. It can be also suitable as a reference for engineers and researchers in the field of systems with jump Markov perturbations. (Vasile Drgan, Mathematical Reviews, January, 2017)

1 Introduction
1(22)
1.1 Motivation and Background
1(2)
1.2 Mathematical Descriptions and Basic Concepts
3(3)
1.3 Practical Examples
6(8)
1.3.1 Solar Thermal Receiver
6(2)
1.3.2 Samuelson's Multiplier-Accelerator Model
8(1)
1.3.3 NASA F-8 Test Aircraft
9(2)
1.3.4 Networked Control Systems
11(3)
1.4 Literature Review
14(5)
1.4.1 Ideal TPs
14(2)
1.4.2 Uncertain TPs
16(1)
1.4.3 Partially Unknown TPs
17(1)
1.4.4 Piecewise Homogeneous TPs
18(1)
1.4.5 Memory TPs
18(1)
1.5 Organization of the Book
19(4)
Part I Partially Unknown TPs
2 Stability and Stabilization
23(22)
2.1 Problem Formulation
23(3)
2.2 Stability
26(7)
2.2.1 Continuous-Time Systems
26(4)
2.2.2 Discrete-Time Systems
30(3)
2.3 Stabilization
33(5)
2.3.1 Continuous-Time Systems
33(2)
2.3.2 Discrete-Time Systems
35(3)
2.4 Numerical Examples
38(6)
2.5 Summary
44(1)
3 H∞ Filtering
45(12)
3.1 Problem Formulation
45(2)
3.2 H∞ Filtering
47(6)
3.2.1 H∞ Filtering Analysis
47(4)
3.2.2 H∞ Filter Design
51(2)
3.3 Numerical Example
53(3)
3.4 Summary
56(1)
4 Time-Delay Systems Case
57(14)
4.1 Problem Formulation
58(1)
4.2 Stability and Stabilization
59(8)
4.3 Numerical Example
67(3)
4.4 Summary
70(1)
5 Composite TPs Case
71(18)
5.1 Introduction
71(2)
5.2 Problem Formulation
73(2)
5.3 Stability
75(6)
5.4 Numerical Examples
81(4)
5.5 Summary
85(4)
Part II Piecewise Homogeneous TPs
6 H∞ Control
89(46)
6.1 Nondeterministic Variations
90(15)
6.1.1 Arbitrary Variation
90(5)
6.1.2 Average Dwell Time Variation
95(10)
6.2 Stochastic Variation
105(6)
6.2.1 Problem Formulation
105(2)
6.2.2 Stochastic Variation
107(2)
6.2.3 A Unified Framework
109(2)
6.3 Systems with Saturation
111(11)
6.3.1 Problem Formulation
111(3)
6.3.2 H∞ Performance Analysis
114(4)
6.3.3 H∞ Output Feedback Controller Design
118(4)
6.4 Numerical Examples
122(11)
6.5 Summary
133(2)
7 Classical and Resilient Filtering
135(38)
7.1 Classical H∞ Filter
136(9)
7.1.1 Problem Formulation
136(2)
7.1.2 Error Performance Analysis
138(3)
7.1.3 A Unified Framework
141(3)
7.1.4 Filter Design
144(1)
7.2 Resilient H∞ Filtering
145(18)
7.2.1 Preliminaries
145(6)
7.2.2 Error Performance Analysis
151(9)
7.2.3 Filter Design
160(3)
7.3 Numerical Examples
163(7)
7.4 Summary
170(3)
8 H∞ Model Reduction
173(16)
8.1 Problem Formulation
173(3)
8.2 H∞ Model Error Performance
176(5)
8.2.1 Type I: Arbitrary Variation
176(1)
8.2.2 Type II: Stochastic Variation
177(2)
8.2.3 A Unified Framework
179(2)
8.3 H∞ Reduced-Order Model Design
181(2)
8.4 Numerical Example
183(1)
8.5 Summary
184(5)
Part III Memory TPs
9 σ-Error Stability and Stabilization
189(18)
9.1 Problem Formulation
189(3)
9.2 Main Results
192(6)
9.3 Numerical Examples
198(6)
9.4 Summary
204(3)
10 Time-Varying Lyapunov Function Approach
207(18)
10.1 Problem Formulation
207(3)
10.2 Stability and Stabilization
210(9)
10.3 Numerical Examples
219(5)
10.4 Summary
224(1)
11 Nonlinear Systems Case
225(24)
11.1 Problem Formulation
225(4)
11.2 Stability and Stabilization
229(11)
11.3 Numerical Examples
240(8)
11.4 Summary
248(1)
References 249(12)
Index 261
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