\(H_\infty\)-control for linear time-delay systems with Markovian jumping parameters
type: Item
instance of: scholarly article
title: \(H_\infty\)-control for linear time-delay systems with Markovian jumping parameters
zbMATH Open document ID: 0971.93027
DOI: 10.1023/A:1004661928043
published in: Journal of Optimization Theory and Applications
publication date: 2001-10-16T00:00:00Z
review text: The goal of the authors is to extend some results concerning an \(H_\infty\)-control problem and its robustness obtained previously for the class of linear time-delay systems to the special linear time-delay systems with Markovian jumping parameters (LTDSMJP). The class of uncertain LTDSMJP with external disturbance is considered. The dynamics of the systems includes state vector, control input, disturbance input, controlled output, the function with a time-delay and norm-bounded uncertainties of two types: nonlinear bounded and norm-bounded uncertainties. Based on a Lyapunov functional approach, a sufficient condition that assures the robust stochastic stabilizability and preserves the \(H_\infty\)-disturbance attenuation of level \(\gamma\) for LTDSMJP is established. The results are based on the solution to a set of coupled algebraic Riccati equations via a combination of the algorithms of Abou-Kandil and Petersen. An illustrative numerical example is presented.
Mathematics Subject Classification ID: 93B36
Mathematics Subject Classification ID: 93D21
Mathematics Subject Classification ID: 93C23
Mathematics Subject Classification ID: 15A39
zbMATH DE Number: 1506898
zbMATH Keywords: Markovian jumping parameters
zbMATH Keywords: stochastic control
zbMATH Keywords: time-delay systems
zbMATH Keywords: Riccati equations
zbMATH Keywords: linear matrix inequalities
zbMATH Keywords: \(H_\infty \)-control problems
zbMATH Keywords: robustness
author: Khalid Benjelloun
author: E. K. Boukas
author: Oswaldo Luiz V. Costa
reviewed by: Yuliya S. Mishura
MaRDI profile type: Publication
cites work: Q3128879
cites work: Mean Square Stochastic Stability Of Linear Time-delay System With Markovian Jumping Parameters
cites work: Stability of stochastic systems with jumps
cites work: Linear minimum mean square error estimation for discrete-time Markovian jump linear systems
cites work: Controllability, stabilizability, and continuous-time Markovian jump linear quadratic control
cites work: Conditions for nonnegativeness of partitioned matrices
cites work: A stabilization algorithm for a class of uncertain linear systems
cites work: Stochastic stability of linear time-delay system with Markovian jumping parameters
cites work: Solution and asymptotic behavior of coupled Riccati equations in jump linear systems
full work available at URL: a:1004661928043
OpenAlex ID: W2283656494
description: scientific article; zbMATH DE number 1506898