Stochastic Switching Systems (eBook)

Analysis and Design

El-Kébir Boukas (Autor)

eBook Download: PDF

2007 | 2006
X, 406 Seiten
Birkhäuser Boston (Verlag)
978-0-8176-4452-9 (ISBN)

Infos

An introductory chapter highlights basics concepts and practical models, which are then used to solve more advanced problems throughout the book.

Included are many numerical examples and LMI synthesis methods and design approaches.

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Stochastic switching systems represent an interesting class, which can be used to model a variety of systems having abrupt random changes in their dynamics. Such systems may be found in the fields of manufacturing, communications, aerospace, power, and economics.This work presents stochastic switching systems and provides up-to-date methods and techniques for the analysis and design of various control systems with or without uncertainties. An introductory chapter highlights basic concepts and practical models, which are then used to solve more advanced problems throughout the book. Included are many numerical examples as well as LMI analysis methods and design approaches to supplement the developed results.Specific topics covered include:*  The stochastic stability problem and its robustness. *  The stabilization problem; different controllers such as the state feedback, output feedback, and observer-based output feedback are designed for nominal and uncertain systems using LMI conditions. *  Systems with external disturbances; different approaches are developed to reject the external disturbances.*  The filtering problem for the class of systems with Markovian jump parameters; Kalman and H-infinity filtering problems are treated and LMI conditions are developed to synthesize the gains of these filters.* Systems with singular Markovian jump parameters. Stochastic Switching Systems may be used as a supplementary textbook for graduate-level engineering courses, or as a reference for control engineers, graduate students, and researchers in systems and control. Prerequisites include elementary courses in matrix theory, probability, optimization techniques, and control systems theory.

Inhalt

Contents 8
Preface 10
1 Introduction 12
1.1 Overview 12
1.2 State-Space Representation 14
1.3 Stochastic Switching Systems 17
1.4 Practical Examples 24
1.5 Organization of the Book 28
1.6 Notation and Abbreviations 29
2 Stability Problem 32
2.1 Problem Statement 33
2.2 Stability 35
2.3 Robust Stability 57
2.4 Stability of Systems with Wiener Process 61
2.5 Notes 71
3 Stabilization Problem 72
3.1 Problem Statement 73
3.2 State Feedback Stabilization 75
3.3 Static Output Feedback Stabilization 99
3.4 Output Feedback Stabilization 106
3.5 Observer-Based Output Stabilization 143
3.6 Stabilization with Constant Gains 177
3.7 Case Study 184
3.8 Notes 189
4 Control Problem 190
4.1 Problem Statement 191
4.2 State Feedback Stabilization 205
4.3 Output Feedback Stabilization 236
4.4 Observer-Based Output Stabilization 263
4.5 Stochastic Systems with Multiplicative Noise 286
4.6 Case Study 315
4.7 Notes 320
5 Filtering Problem 322
5.1 Problem Statement 323
5.2 Kalman Filtering 325
5.3 339
Filtering 339
5.4 Notes 362
6 Singular Stochastic Switching Systems 364
6.1 Problem Statement 364
6.2 Stability Problem 368
6.3 Stabilization Problem 373
6.4 Constant Gain Stabilization 381
6.5 Notes 385
Appendix A Mathematical Review 386
A.1 Linear Algebra 386
A.2 Matrix Theory 388
A.3 Markov Process 393
A.4 Lemmas 403
References 408
Index 412

Textauszug

3 Stabilization Problem (p. 61-62)

One of the most popular control problems, the stabilization problem consists of determining a control law that forces the closed-loop state equation of a given system to guarantee the desired design performances. This problem has and continues to attract many researchers from the control community and many techniques can be used to solve the stabilization problem for dynamical systems. From the practical point of view when designing any control system, the stabilization problem is the most important in the design phase since it will give the desired performances to the designed control system. The concepts of stochastic stability and its robustness for the class of piecewise deterministic systems were presented in the previous chapter. Most of the developed results are LMI-based conditions that can be used easily to check if a dynamical system of the class we are considering is stochastically stable and robustly stochastically stable.

In practice some systems are unstable or their performances are not acceptable. To stabilize or improve the performances of such systems, we examine the design of an appropriate controller. Once combined with the system this controller should stabilize the closed loop and at the same time guarantee the required performances.

In the literature, we can .nd di.erent techniques of stabilization that can be divided into two groups. The .rst group gathers all the techniques that assume the complete access to the state vector and the other group is composed of techniques that are based on partial state vector observation. For the class of systems under consideration, the following techniques can be used:

- state feedback stabilization,
- ,output feedback stabilization.

This chapter will focus on these two techniques and develop LMI-based procedures to design the corresponding gains. The rest of this chapter is organized as follows. In Section 3.1, the stabilization problem is stated and some useful de.nitions are given. Section 3.2 treats the state feedback stabilization for nominal and uncertain classes of piecewise deterministic systems. Section 3.3 covers the stabilization with the static output feedback controller. In Section 3.4, output feedback is covered. Section 3.5 deals with observer-output feedback stabilization. Section 3.6 develops the design of the state feedback controller with constant gain. All the developed results are in LMI framework, which makes the resolution of the stabilization problem easier. Many numerical examples are provided to show the usefulness of the developed results.

Produkt-Details

• Erscheint lt. Verlag: 24.5.2007
• Reihe/Serie: Control Engineering
• Reihe/Serie: Control Engineering
• Zusatzinfo: X, 406 p. 7 illus.
• Verlagsort: Boston
• Sprache: englisch
• Themenwelt: Informatik ► Theorie / Studium ► Künstliche Intelligenz / Robotik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Statistik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
• Themenwelt: Technik ► Elektrotechnik / Energietechnik
• Themenwelt: Technik ► Maschinenbau
• Schlagworte: Analysis • Communication • filtering problem • Markov • matrix theory • Model • Optimization • stability • Systems Theory
• ISBN-10: 0-8176-4452-0 / 0817644520
• ISBN-13: 978-0-8176-4452-9 / 9780817644529