Necessary and sufficient condition for robust stability and stabilizability of continuous-time linear systems with Markovian jumps
type: Item
instance of: scholarly article
title: Necessary and sufficient condition for robust stability and stabilizability of continuous-time linear systems with Markovian jumps
zbMATH Open document ID: 0919.93082
DOI: 10.1023/A:1021722210476
published in: Journal of Optimization Theory and Applications
publication date: 1999-09-05T00:00:00Z
review text: The goal of this paper is to derive a necessary and sufficient condition for mean-square quadratic stability and stabilizability for continuous-time linear stochastic systems with Markovian jumps. The systems are described by the following differential equation, \[ \dot x(t)= [A(r(t))+\Delta A(r(t),t)] x(t)+ [B(r(t))+\Delta B(r(t),t)] u(t),\quad x(0)= x_0,\;r(0)= r_0, \] where \(x(t)\in \mathbb{R}^n\) is the state, \(u(t)\in\mathbb{R}^m\) is the control input, \(\Delta A\) and \(\Delta B\) are system uncertainties, the term \(r(t)\) is a continuous-time stochastic Markovian process with finite discrete state space. The criterion of mean-square quadratic robust stability is established for the autonomous system with \(u= 0\), and the criterion of quadratic stabilizability is established in the case of a feedback control of the form \(u(t)= K(r(t)) x(t)\). A quadratic guaranteed cost control problem with the same \(u(t)\) and \(K= (K(1),\dots, K(N))\) is also investigated.
Mathematics Subject Classification ID: 93E15
Mathematics Subject Classification ID: 93D09
Mathematics Subject Classification ID: 93D21
Mathematics Subject Classification ID: 60J25
zbMATH DE Number: 1239677
zbMATH Keywords: parametric uncertainties
zbMATH Keywords: Riccati equation
zbMATH Keywords: Markovian jumps
zbMATH Keywords: mean-square quadratic robust stability
zbMATH Keywords: quadratic stabilizability
author: Oswaldo Luiz V. Costa
author: E. K. Boukas
reviewed by: Yuliya S. Mishura
MaRDI profile type: Publication
cites work: Robust stabilization of uncertain linear systems: quadratic stabilizability and H/sup infinity / control theory
cites work: A stabilization algorithm for a class of uncertain linear systems
cites work: Optimal guaranteed cost control and filtering for uncertain linear systems
cites work: Robust production and maintenance planning in stochastic manufacturing systems
cites work: Controllability, stabilizability, and continuous-time Markovian jump linear quadratic control
cites work: Stochastic stability properties of jump linear systems
cites work: Continuous-time state-feedback \(H_2\)-control of Markovian jump linear systems via convex analysis
cites work: Stability of discrete-time linear systems with Markovian jumping parameters
cites work: Stability of stochastic systems with jumps
cites work: Optimal stationary control for dynamic systems with Markov perturbations
cites work: Stability and control for linear systems with jump Markov perturbations
cites work: Parametrized riccati equations for controlled linear differential systems with jump Markov perturbations
cites work: \(H_\infty\)-control for Markovian jumping linear systems with parametric uncertainty
cites work: Quadratic stability and stabilization of linear systems with Frobenius norm-bounded uncertainties
description: scientific article; zbMATH DE number 1239677