Stabilization of Singular Markovian Jump Systems With Generally Uncertain Transition Rates

This note is devoted to investigating the stability and stabilization problems for continuous-time singular Markovian jump systems (SMJSs) with generally uncertain transition rates (GUTRs). In this GUTR singular model, each transition rate can be completely unknown or only its estimate value is know...

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Bibliographic Details
Published in:IEEE transactions on automatic control 2014-09, Vol.59 (9), p.2604-2610
Main Authors: Kao, Yonggui, Xie, Jing, Wang, Changhong
Format: Article
Language:English
Subjects:
Closed loop systems
Control systems
Estimates
Joining
Linear matrix inequalities
Markov processes
Mathematical models
Numerical stability
Probability theory
Randomness
Stability criteria
Stabilization
Stochastic processes
Symmetric matrices
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Summary:This note is devoted to investigating the stability and stabilization problems for continuous-time singular Markovian jump systems (SMJSs) with generally uncertain transition rates (GUTRs). In this GUTR singular model, each transition rate can be completely unknown or only its estimate value is known. In terms of a set of coupled linear matrix inequalities (LMIs), a sufficient condition is established to ensure the systems to be regular, impulse-free and stochastically stable. Moreover, the corresponding sufficient condition on the existence of a mode-dependent state-feedback controller is derived to guarantee the closed-loop systems stochastically admissible by applying the LMI technique. Finally, a numerical example is presented to illustrate the effectiveness and efficiency of the proposed method.
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2014.2313756