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

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4 Author(s)
Zuo, Z. ; Tianjin Key Lab. of Process Meas. & Control, Tianjin Univ., Tianjin, China ; Liu, Y. ; Wang, Y. ; Li, H.

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.

Published in:

Control Theory & Applications, IET  (Volume:6 ,  Issue: 10 )