Necessary and sufficient condition for robust stability and stabilizability of continuous-time linear systems with Markovian jumps

DOI10.1023/A:1021722210476zbMath0919.93082MaRDI QIDQ1275708

Oswaldo L. V. Costa, El-Kébir Boukas

Publication date: 5 September 1999

Published in: Journal of Optimization Theory and Applications (Search for Journal in Brave)

zbMATH Keywords

Markovian jumpsRiccati equationquadratic stabilizabilityparametric uncertaintiesmean-square quadratic robust stability

Mathematics Subject Classification ID

Continuous-time Markov processes on general state spaces (60J25) Adaptive or robust stabilization (93D21) Robust stability (93D09) Stochastic stability in control theory (93E15)

Related Items (11)

Delay-dependent \(H_\infty\) filtering of uncertain Markovian jump delay systems via delay-partitioning approach ⋮ Approximations of Euler-Maruyama type for stochastic differential equations with Markovian switching, under non-Lipschitz conditions ⋮ GeneralizedH₂control of the linear system with semi‐Markov jumps ⋮ Guaranteed cost control of a Markov jump linear uncertain system using a time-multiplied cost function ⋮ Convergence of the Euler--Maruyama method for stochastic differential equations with Markovian switching. ⋮ On robust H_∞ filtering of uncertain Markovian jump time‐delay systems ⋮ Stationary distributions of Euler–Maruyama-type stochastic difference equations with Markovian switching and their convergence ⋮ Numerical method for stationary distribution of stochastic differential equations with Markovian switching ⋮ Temporal difference methods for the maximal solution of discrete-time coupled algebraic Riccati equations ⋮ Delay-dependent stability and \(h_{\infty }\) control of uncertain discrete-time Markovian jump systems with mode-dependent time delays ⋮ A new look at the robust control of discrete-time Markov jump linear systems

Cites Work

• A stabilization algorithm for a class of uncertain linear systems
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• Stability of stochastic systems with jumps
• \(H_\infty\)-control for Markovian jumping linear systems with parametric uncertainty
• Stability of discrete-time linear systems with Markovian jumping parameters
• Optimal stationary control for dynamic systems with Markov perturbations
• Controllability, stabilizability, and continuous-time Markovian jump linear quadratic control
• Robust stabilization of uncertain linear systems: quadratic stabilizability and H/sup infinity / control theory
• Stochastic stability properties of jump linear systems
• Parametrized riccati equations for controlled linear differential systems with jump Markov perturbations
• Optimal guaranteed cost control and filtering for uncertain linear systems
• Stability and control for linear systems with jump Markov perturbations
• Robust production and maintenance planning in stochastic manufacturing systems
• Quadratic stability and stabilization of linear systems with Frobenius norm-bounded uncertainties

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