Control of uncertain sampled-data systems
著者
書誌事項
Control of uncertain sampled-data systems
（Systems & control）
Birkhäuser, 1996
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注記
Bibliography: p. 171-177
内容説明・目次
- 巻冊次
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ISBN 9780817638511
内容説明
My main goal in writing this monograph is to provide a detailed treatment of uncertainty analysis for sampled-data systems in the context of sys tems control theory. Here, sampled-data system refers to the hybrid sys tem formed when continuous time and discrete time systems are intercon nected; by uncertainty analysis I mean achievable performance in the pres ence of worst -case uncertainty and disturbances. The focus of the book is sampled-data systems; however the approach presented is applicable to both standard and sampled-data systems. The past few years has seen a large surge in research activity centered around creating systematic methods for sampled-data design. The aim of this activity has been to deepen and broaden the, by now, sophisticated viewpoint developed for design of purely continuous time or discrete time systems (e.g. J{oo or -I!l optimal synthesis, J1 theory) so that it can be ap plied to the design of sampled-data systems. This research effort has been largely successful, producing both interesting new mathematical tools for control theory, and new methodologies for practical engineering design. Analysis of structured uncertainty is an important objective in control design, because it is a flexible and non-conservative way of analyzing sys tem performance, which is suitable in many engineering design scenarios.
目次
1 Introduction.- 1.1 Modelling and Uncertainty.- 1.2 Summary of Contents.- 2 Preliminaries.- 2.1 Hilbert Space and Banach Algebras.- 2.2 Operator Theory.- 2.3 Analytic Functions.- 2.4 Time Domain Spaces and Lifting.- 2.5 Frequency Domain Function Spaces.- 2.6 The Structured Singular Value.- 3 Uncertain Sampled-data Systems.- 3.1 Summary.- 4 Analysis of LTI Uncertainty.- 4.1 Converting to Frequency Domain.- 4.2 Destabilizing Perturbations.- 4.3 Robustness Test.- 4.4 Sampled-data Frequency Response.- 4.5 Summary.- 5 A Computational Framework.- 5.1 Lower Bounds.- 5.2 Upper Bounds.- 5.3 An Algorithm.- 5.4 Example.- 5.5 Summary.- 6 Robust Performance.- 6.1 Robust Performance Conditions.- 6.2 Computational Tools.- 6.3 Example Algorithm.- 6.4 Minimizing the Scaled Hilbert-Schmidt Norm.- 6.5 Summary.- A State space for ?M.- B Proof of Proposition 5.4.- D State Space for Section 6.2.- E Proof of Lemma 6.10.- G The S-Procedure.
- 巻冊次
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ISBN 9783764338510
内容説明
Hybrid systems are formed when continuous-time and discrete-time systems are interconnected. The author's goal in this text is to provide a treatment of uncertainty analysis for samle-data hybrid systems in the context of robust control theory. The book has a general scope in that it offers a widely applicable and unifying viewpoint that considers a large class of structured uncertainty problems arising in control, whether the system be hybrid, discrtete-time or continuous-time. In the body of the text, operator theoretic tools and techniques are developed to address the central design issues of performance and stabilization in the presence of structured uncertainty classes. The methods are applied to exact analysis of hybrid sampled-data systems in the H-infinity or Hilbert space setting, with the focus being mu-theory and its generalizations to time-varying uncertainty structures. The mathematical machinery and framework presented provide a unified approach to studying performance and uncertainty, and is applicable to both standard and sampled-data systems.
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