Finite-time H∞ control for stochastic time-delayed Markovian switching systems with partly known transition rates and nonlinearity

This paper focuses on the problem of finite-time H∞ control for stochastic time-delayed Markovian switching systems with partly known transition rates and nonlinearity. By employing an appropriate Lyapunov function and some appropriate free-weighting matrices, a state feedback controller is designed to ensure H∞ finite-time boundedness of the resulting closed-loop system that contains time-varying delay, admissible external disturbance, It -type stochastic disturbance and nonlinearity. All the proposed conditions are established in the form of linear matrix inequalities. Finally, an example is given to demonstrate the validity of the main results.

[1]  Yuzhen Wang,et al.  Finite-time stability analysis and H∞ control for a class of nonlinear time-delay Hamiltonian systems , 2013, Autom..

[2]  Hanyong Shao.  Delay-range-dependent robust H∞ filtering for uncertain stochastic systems with mode-dependent time delays and Markovian jump parameters , 2008 .

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

[4]  Yongduan Song,et al.  Finite-time H∞ filtering for discrete-time Markovian jump systems , 2013, J. Frankl. Inst..

[5]  Guoliang Wang.  Partially mode-dependent design of H∞ filter for stochastic Markovian jump systems with mode-dependent time delays☆ , 2011 .

[6]  Zhiqiang Zuo,et al.  Robust H ∞ control of discrete-time Markovian jump systems in the presence of incomplete knowledge of transition probabilities and saturating actuator , 2012 .

[7]  Caixia Liu,et al.  Observer-based finite-timeH∞control of discrete-time Markovian jump systems , 2013, Applied Mathematical Modelling.

[8]  Ju H. Park,et al.  Stochastic stability analysis for discrete-time singular Markov jump systems with time-varying delay and piecewise-constant transition probabilities , 2012, J. Frankl. Inst..

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

[10]  Chunhui Wang,et al.  Controller synthesis for Markovian jump systems with incomplete knowledge of transition probabilities and actuator saturation , 2011, J. Frankl. Inst..

[11]  Zidong Wang,et al.  Exponential Stabilization of a Class of Stochastic System With Markovian Jump Parameters and Mode-Dependent Mixed Time-Delays , 2010, IEEE Transactions on Automatic Control.

[12]  Yong He,et al.  State estimation for Markovian jump systems with time-varying delay and partial information on transition probabilities [Brief Paper] , 2012 .

[13]  Max Q.-H. Meng,et al.  Robust H∞ exponential filtering for uncertain stochastic time-delay systems with Markovian switching and nonlinearities , 2010, Appl. Math. Comput..

[14]  José Claudio Geromel,et al.  Output feedback control of Markov jump linear systems in continuous-time , 2000, IEEE Trans. Autom. Control..

[15]  Xinzhi Liu,et al.  Stability analysis for neutral Markovian jump systems with partially unknown transition probabilities , 2012, J. Frankl. Inst..

[16]  S. Zhong,et al.  Finite-time H∞ control for a class of Markovian jump systems with mode-dependent time-varying delay , 2013, Advances in Difference Equations.

[17]  Pagavathigounder Balasubramaniam,et al.  H∞ Filtering for Markovian Switching System with Mode-Dependent Time-Varying Delays , 2014, Circuits Syst. Signal Process..

[18]  X. Mao.  Stability of stochastic differential equations with Markovian switching , 1999 .

[19]  Francesco Amato,et al.  Finite-time control of discrete-time linear systems: Analysis and design conditions , 2010, Autom..

[20]  Wei Xing Zheng,et al.  Robust ℋ∞ filtering of Markovian jump stochastic systems with uncertain transition probabilities , 2011, Int. J. Syst. Sci..

[21]  Dandan Wang,et al.  Non-fragile observer-based sliding mode control for Markovian jump systems with mixed mode-dependent time delays and input nonlinearity , 2014, Appl. Math. Comput..

[22]  Pagavathigounder Balasubramaniam,et al.  L2-L∞L2-L∞ Filtering for neutral Markovian switching system with mode-dependent time-varying delays and partially unknown transition probabilities , 2013, Appl. Math. Comput..

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

[24]  P. Balasubramaniam,et al.  Delay-Dependent Robust Stabilization and H∞ Control for Nonlinear Stochastic Systems with Markovian Jump Parameters and Interval Time-Varying Delays , 2011, J. Optim. Theory Appl..

[25]  Fei Liu,et al.  Observer-based finite-time control of time-delayed jump systems , 2010, Appl. Math. Comput..

[26]  Won-jong Kim,et al.  Markov-chain-based output feedback control for stabilization of networked control systems with random time delays and packet losses , 2012 .

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

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

[29]  Zhigang Zeng,et al.  Observer‐based H ∞  control of discrete Markovian jump delay systems with random packet losses and multiplicative noises , 2013 .

[30]  Shouming Zhong,et al.  H∞ Filtering for Stochastic Systems with Markovian Switching and Partly Unknown Transition Probabilities , 2012, Circuits, Systems, and Signal Processing.

[31]  Zidong Wang,et al.  Robust H∞ control of stochastic time‐delay jumping systems with nonlinear disturbances , 2006 .

[32]  Jing Wang,et al.  Finite-time H∞ control for a class of Markovian jump delayed systems with input saturation , 2013 .

[33]  Keith J. Burnham,et al.  On stabilization of bilinear uncertain time-delay stochastic systems with Markovian jumping parameters , 2002, IEEE Trans. Autom. Control..

[34]  Huijun Gao,et al.  New results on stabilization of Markovian jump systems with time delay , 2009, Autom..

[35]  Bing Chen,et al.  A Delay-Dependent Approach to Robust H∞ Control for Uncertain Stochastic Systems with State and Input Delays , 2009, Circuits Syst. Signal Process..

[36]  Shengyuan Xu,et al.  Robust stochastic stabilization and H∞ control of uncertain neutral stochastic time-delay systems☆ , 2006 .

[37]  Zhiqiang Zuo,et al.  Finite-time stochastic stability and stabilisation of linear discrete-time Markovian jump systems with partly unknown transition probabilities , 2012 .

[38]  Shengyuan Xu,et al.  A NEW LMI CONDITION FOR DELAY‐DEPENDENT ROBUST STABILITY OF STOCHASTIC TIME‐DELAY SYSTEMS , 2005 .

[39]  Fei Liu,et al.  On Delay-Dependent Stability of Markov Jump Systems with Distributed Time-Delays , 2011, Circuits Syst. Signal Process..