Analysis and synthesis of singular systems with time-delays
type: Item
instance of: scholarly article
title: Analysis and synthesis of singular systems with time-delays
zbMATH Open document ID: 1362.93001
DOI: 10.1007/978-3-642-37497-5
author: Zhengguang Wu
author: Peng Shi
author: Jian Chu
author: Hongye Su
published in: Lecture Notes in Control and Information Sciences
publication date: 2013-05-29T00:00:00Z
review text: After a detailed description of predecessor results on singular nonlinear systems and especially on Markov jump systems (MJSs) and singular MJSs (SMJSs), and a short presentation of the obtained results in the chapters, the authors turn to part I Singular systems (SSs) with time delays and part II SMJSs. The basic content of this monograph are recent advances in analysis and synthesis of singular time-delayed systems with or without Markov jumping parameters. In Ch. 2 using the method of linear matrix inequalities (LMI) and a finite sum inequality the delay-dependent and independent robust control problems for discrete time SSs with time delay and norm bounded parametric uncertainties are studied with the aim to obtain a state feedback controller for the system to be regular causal and stable for all uncertainties. The obtained results are illustrated by two numerical examples. In Ch. 3 the continuous time SSs with time delay of the following form are considered \[ E \dot{x}(t) = Ax(t)+A_{d}x(t-d)+B_{w}w(t), \quad x(t)=\varphi (t), t\in[-d,0] \] where \(z(t) = Cx(t)+Du(t)\) is the controlled output, \(u(t)\) is the control input, and \(\text{rank}\,E = r \leq n\), \(A, A_{d}, B, B_{w}, C, D\) are constant matrices. In using the LMI approach and an augmented Lyapunov functional the problem of delay-dependent state feedback \(H_{\infty}\) control is solved. In Ch. 4 similar systems but with time-varying delays \(d=d(t)\) and actuator failures are studied with the aim to establish the time-dependent condition for the system would be regular, impulse free, exponentially stable and passive. Numerical examples are given. As in Ch. 3 an explicit expression for the desired controller is obtained. Ch. 5 is devoted to dissipativity analysis for SSs with time-varying delays of the previous form and also for discrete time SSs with discrete and distributed time-varying delays. The definitions of dissipativity property are introduced using the notion of energy supply function. In…
Mathematics Subject Classification ID: 93-02
Mathematics Subject Classification ID: 93B50
Mathematics Subject Classification ID: 93C23
Mathematics Subject Classification ID: 93E11
zbMATH DE Number: 6167988
reviewed by: Boris V. Loginov
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/978-3-642-37497-5
OpenAlex ID: W562253250
description: scientific article; zbMATH DE number 6167988