Finite-time stochastic stability and stabilisation of linear discrete-time Markovian jump systems with partly unknown transition probabilities

This study deals with the problems of finite-time stochastic stability and stabilisation with partly unknown transition probabilities for linear discrete-time Markovian jump systems (MJP). The definition of finite-time stochastic stability for discrete-time MJP is firstly given. Based on it, a sufficient condition is proposed to guarantee that the state of the system does not exceed a certain threshold in mean-square sense during a specified time interval. The above result is then extended to the finite-time stochastic stabilisation case. By introducing some free-weighting matrices, the proposed method leads to less conservatism compared with the existing ones. Two numerical examples are given to illustrate the effectiveness of the proposed methods.

[1]  W. L. Koning,et al.  Discrete-time Markovian jump linear systems , 1993 .

[2]  Dennis S. Bernstein,et al.  Finite-Time Stability of Continuous Autonomous Systems , 2000, SIAM J. Control. Optim..

[3]  Francesco Amato,et al.  Finite-time control of linear systems subject to parametric uncertainties and disturbances , 2001, Autom..

[4]  Francesco Amato,et al.  Finite-time control of discrete-time linear systems , 2005, IEEE Transactions on Automatic Control.

[5]  James Lam,et al.  On robust stabilization of Markovian jump systems with uncertain switching probabilities , 2005, Autom..

[6]  Carlo Cosentino,et al.  Finite-time stabilization via dynamic output feedback, , 2006, Autom..

[7]  Peng Shi,et al.  Transition probability bounds for the stochastic stability robustness of continuous- and discrete-time Markovian jump linear systems , 2006, Autom..

[8]  Shengyuan Xu,et al.  Robust stabilization of Markovian delay systems with delay-dependent exponential estimates , 2006, Autom..

[9]  James Lam,et al.  Analysis and Synthesis of Markov Jump Linear Systems With Time-Varying Delays and Partially Known Transition Probabilities , 2008, IEEE Transactions on Automatic Control.

[10]  Lixian Zhang,et al.  Stability and stabilization of Markovian jump linear systems with partly unknown transition probabilities , 2009, Autom..

[11]  Lixian Zhang,et al.  Mode-dependent Hinfinity filtering for discrete-time Markovian jump linear systems with partly unknown transition probabilities , 2009, Autom..

[12]  E. Boukas,et al.  H∞ control for discrete‐time Markovian jump linear systems with partly unknown transition probabilities , 2009 .

[13]  Daniel W. C. Ho,et al.  Fault tolerant control for singular systems with actuator saturation and nonlinear perturbation , 2010, Autom..