Theory of control systems described by differential inclusions
type: Item
instance of: scholarly article
title: Theory of control systems described by differential inclusions
zbMATH Open document ID: 1362.49002
DOI: 10.1007/978-3-662-49245-1
author: Jun Huang
author: Zhengzhi Han
author: Xiushan Cai
published in: Springer Tracts in Mechanical Engineering
publication date: 2016-07-12T00:00:00Z
review text: The first chapter introduces the fundamental concepts and conclusions of functional analysis so that readers can have a foundation for going on reading this book successfully and can also understand notations used in the book. The arrangement of this chapter is as follows: The first section deals with normed linear spaces and inner product spaces which both provide a platform for further investigation; the second section introduces convex sets, and the third section considers convex functions; the last section of this chapter introduces semi-continuous functions. These are all necessary for research of set-valued mappings and differential inclusions which are two key concepts in this book. The most materials given in this chapter are referred to [\textit{J. B. Conway}, A course in functional analysis. New York, NY: Springer-Verlag (1985; Zbl 0558.46001)] which has been widely used in Chinese universities. Chapter 2 deals with two fundamental concepts for the control systems described by differential inclusions. They are set-valued mappings and differential inclusions. The first two sections introduce the set-valued mappings and the succeeding four sections involve the differential inclusions. In Chapter 3, the authors deal with several kinds of differential inclusions and their control. They recall that mathematical investigation in many fields starts from the linear case; for example, at the beginning of control theory, one deals with the linear system, the functional analysis starts with the linear normed spaces and linear mappings. Consequently, the authors consider convex processes which can be treated as an extension of the linear single-valued mapping to set-valued mapping. They consider linear polytopic differential inclusions and the Lur'e systems. This can also be thought as extensions of linear control systems to differential inclusions and nonlinear differential inclusions. The organization of this chapter is as follows. At the first section, convex proce…
reviewed by: Rita Pini
Mathematics Subject Classification ID: 49-02
Mathematics Subject Classification ID: 34A60
Mathematics Subject Classification ID: 49J21
Mathematics Subject Classification ID: 93-02
Mathematics Subject Classification ID: 93D15
Mathematics Subject Classification ID: 46-02
Mathematics Subject Classification ID: 49J53
Mathematics Subject Classification ID: 26E25
zbMATH DE Number: 6603154
zbMATH Keywords: convex functions
zbMATH Keywords: set-valued mappings
zbMATH Keywords: differential inclusions
zbMATH Keywords: convex processes
zbMATH Keywords: linear polytope systems
zbMATH Keywords: Lur'e differential inclusion systems
zbMATH Keywords: Luenberger observers
zbMATH Keywords: control systems
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/978-3-662-49245-1
OpenAlex ID: W2485658472
description: scientific article; zbMATH DE number 6603154