Title :
Analysis and Synthesis of Markov Jump Linear Systems With Time-Varying Delays and Partially Known Transition Probabilities
Author :
Zhang, Lixian ; Boukas, El-Kébir ; Lam, James
Author_Institution :
Space Control & Inertial Technol. Res. Center, Harbin Inst. of Technol., Harbin
Abstract :
In this note, the stability analysis and stabilization problems for a class of discrete-time Markov jump linear systems with partially known transition probabilities and time-varying delays are investigated. The time-delay is considered to be time-varying and has a lower and upper bounds. The transition probabilities of the mode jumps are considered to be partially known, which relax the traditional assumption in Markov jump systems that all of them must be completely known a priori. Following the recent study on the class of systems, a monotonicity is further observed in concern of the conservatism of obtaining the maximal delay range due to the unknown elements in the transition probability matrix. Sufficient conditions for stochastic stability of the underlying systems are derived via the linear matrix inequality (LMI) formulation, and the design of the stabilizing controller is further given. A numerical example is used to illustrate the developed theory.
Keywords :
Markov processes; delays; discrete time systems; linear matrix inequalities; linear systems; stability; stochastic systems; discrete-time Markov jump linear systems; linear matrix inequality; partially known transition probabilities; stability analysis; stabilizing controller; stochastic stability; time-varying delays; transition probability matrix; Control systems; Delay effects; Delay systems; Linear matrix inequalities; Linear systems; Mechanical engineering; Space technology; Stability; Stochastic systems; Time varying systems; Linear matrix inequality (LMI); Markov jump linear systems; stochastic stability and stabilization; time-varying delays; transition probabilities;
Journal_Title :
Automatic Control, IEEE Transactions on
DOI :
10.1109/TAC.2008.2007867