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Über dieses Buch

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.

Inhaltsverzeichnis

Frontmatter

Chapter 1. Introduction

Abstract
This monograph is concerned with the analysis of uncertain sampled-data systems which arise in control theory.
Geir E. Dullerud

Chapter 2. Preliminaries

Abstract
This chapter is devoted to collecting the mathematical facts and tools required subsequently. The first three sections cover primarily standard results from linear analysis, whereas the remaining three sections provide technical background specific to the analysis of uncertain sampled-data systems.
Geir E. Dullerud

Chapter 3. Uncertain Sampled-data Systems

Abstract
In this chapter we introduce the general sampled-data system configuration considered in this work. The system arrangement is shown in Figure 3.1. The figure shows a continuous time system G in feedback with a discrete time controller Kd through the sample and hold devices defined in (2.2). Also in feedback with G is the block diagonal system diag(Δ1,..., Δd), referred to as simply Δ, which represents uncertainty in the connected system. The system G is assumed to be a finite dimensional linear time-invariant (FDLTI) continuous time system; the discrete time controller Kd is also FDLTI.
Geir E. Dullerud

Chapter 4. Analysis of LTI Uncertainty

Abstract
Our intent now is to construct a robust stability condition which characterizes system robustness to stable LTI perturbations. Furthermore, we continue to develop a general framework in which to consider issues of robustness for sampled-data systems.
Geir E. Dullerud

Chapter 5. A Computational Framework

Abstract
The main robustness result of the previous chapter is a both necessary and sufficient condition for robust stabilization of a sampled-data system to structured LTI perturbations. The condition is given in terms of the structured singular value of the sampled-data system frequency response µ Δ LTI (M(e )) evaluated on the unit circle. The capability to use this stability test therefore relies on the ability to effectively evaluate the structured singular value of the infinite dimensional operator M(e ). This chapter is aimed at developing a computational framework that addresses this task. The approach used is to obtain bounds: we construct a family of upper and lower bounds for µ Δ LTI (M(e )) whose members converge to µ Δ LTI (M(e )). The resulting computational procedure is one in which the accuracy of the bounds for µ Δ LTI (M(e )) can be systematically improved at the cost of additional computational effort.
Geir E. Dullerud

Chapter 6. Robust Performance

Abstract
We have considered robust stabilization to LTI perturbations; that is, perturbations which do not vary with time. In this chapter we concentrate on three expanded perturbation classes each permitting a different level of time variation. We focus on robust performance analysis of sampled-data systems which are subject to perturbations that are periodic in the sampling rate of the nominal system, quasi-periodic and arbitrary time-varying.
Geir E. Dullerud

Backmatter

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