Finite-time stochastic stabilization for uncertain Markov jump systems subject to input constraint

In this paper, the problem of finite-time stochastic stabilization for a class of uncertain Markov jump systems subject to partly known transition probabilities and disturbances is investigated. The constraint on the control input sent to the actuator is also considered. A finite-time stochastic stabilization criterion is given, to ensure that the state trajectory remains in a bounded region of the state space over a fixed time interval in mean square sense. An optimization algorithm is proposed to find the optimal performance and the corresponding feedback controller where the undesirable high-gain phenomenon can be avoided. Finally, numerical examples are given to illustrate the effectiveness of the proposed method.

[1]  Yi Liu,et al.  On Finite-Time Stochastic Stability and Stabilization of Markovian Jump Systems Subject to Partial Information on Transition Probabilities , 2012, Circuits Syst. Signal Process..

[2]  E. Boukas,et al.  Mode-dependent Hºº filtering for discrete-time Markovian jump linear systems with partly unknown transition probabilities. , 2007 .

[3]  Jie Zhang,et al.  Stabilization for Markovian jump systems with partial information on transition probability based on free-connection weighting matrices , 2011, Autom..

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

[5]  El-Kébir Boukas,et al.  Stochastic Switching Systems: Analysis and Design , 2005 .

[6]  James Lam,et al.  Robust Control of Uncertain Markovian Jump Systems with Time-Delay , 2000 .

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

[9]  Robin J. Evans,et al.  Continuous direct adaptive control with saturation input constraint , 1994, IEEE Trans. Autom. Control..

[10]  Peng Shi,et al.  Control of Markovian jump discrete-time systems with norm bounded uncertainty and unknown delay , 1999, IEEE Trans. Autom. Control..

[11]  Yugang Niu,et al.  Stabilization of Markovian jump linear system over networks with random communication delay , 2009, Autom..

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

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

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

[15]  P. Dorato.  SHORT-TIME STABILITY IN LINEAR TIME-VARYING SYSTEMS , 1961 .

[16]  Zidong Wang,et al.  State estimation for Markov-type genetic regulatory networks with delays and uncertain mode transition rates , 2009 .

[17]  James Lam,et al.  Necessary and Sufficient Conditions for Analysis and Synthesis of Markov Jump Linear Systems With Incomplete Transition Descriptions , 2010, IEEE Transactions on Automatic Control.

[18]  Haiping Du,et al.  Fuzzy Control for Nonlinear Uncertain Electrohydraulic Active Suspensions With Input Constraint , 2009, IEEE Trans. Fuzzy Syst..

[19]  I. Petersen.  A stabilization algorithm for a class of uncertain linear systems , 1987 .

[20]  E. Boukas,et al.  Stability and Stabilization of Markovian Jump Linear Systems with Partly Unknown Transition Probabilities , 2008 .

[21]  Guang-Hong Yang,et al.  Robust H2 control of continuous-time Markov jump linear systems , 2008, Autom..

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