Nonfragile observer‐based H ∞  sliding mode control for Itô stochastic systems with Markovian switching

The paper is devoted to investigating sliding mode control for a class of nonlinear uncertain stochastic systems with input nonlinearity and Markovian switching. A nonfragile observer subjected to the transition rates of the modes is designed. By some specified matrices, the connections among the designed sliding surfaces corresponding to every mode are established. The state estimation‐based sliding mode control law is derived to guarantee the reachability of the sliding surface in finite time interval. The sufficient conditions on asymptotically stochastic stability of the error system and sliding mode dynamics with a given disturbance attenuation level are derived in terms of linear matrix inequalities. Finally, an example is provided to illustrate the efficiency of the proposed method. Copyright © 2013 John Wiley & Sons, Ltd.

[1]  Linear discrete-time system stability under parameter variations , 1984 .

[2]  Vadim I. Utkin,et al.  Sliding Modes in Control and Optimization , 1992, Communications and Control Engineering Series.

[3]  Kou-Cheng Hsu Variable Structure Control Design for Uncertain Dynamic Systems with Sector Nonlinearities , 1998, Autom..

[4]  Hung-Yuan Chung,et al.  Fuzzy sliding mode controller design for uncertain time-delayed systems with nonlinear input , 2003, Fuzzy Sets Syst..

[5]  Yuanqing Xia,et al.  Robust sliding-mode control for uncertain time-delay systems: an LMI approach , 2003, IEEE Trans. Autom. Control..

[6]  Michael Basin,et al.  Integral sliding mode design for robust filtering and control of linear stochastic time‐delay systems , 2005 .

[7]  Dong Yue,et al.  Delay-dependent exponential stability of stochastic systems with time-varying delay, nonlinearity, and Markovian switching , 2005, IEEE Transactions on Automatic Control.

[8]  Yuanqing Xia,et al.  Robust adaptive sliding mode control for uncertain time-delay systems , 2006, 2006 American Control Conference.

[9]  Yuanqing Xia,et al.  On designing of sliding-mode control for stochastic jump systems , 2006, IEEE Transactions on Automatic Control.

[10]  Wang Changhong,et al.  Sliding mode H∞ control for a class of uncertain nonlinear state-delayed systems , 2006 .

[11]  Daniel W. C. Ho,et al.  Robust observer design for Itô stochastic time-delay systems via sliding mode control , 2006, Syst. Control. Lett..

[12]  James Lam,et al.  Robust energy-to-peak filter design for stochastic time-delay systems , 2006, Syst. Control. Lett..

[13]  T. Floquet,et al.  On Sliding Mode Observers for Systems with Unknown Inputs , 2006, International Workshop on Variable Structure Systems, 2006. VSS'06..

[14]  Guanrong Chen,et al.  New criteria for synchronization stability of general complex dynamical networks with coupling delays , 2006 .

[15]  Xingyu Wang,et al.  Sliding mode control for Itô stochastic systems with Markovian switching , 2007, Autom..

[16]  Huijun Gao,et al.  ℋ︁∞ and l2–l∞ filtering for two‐dimensional linear parameter‐varying systems , 2007 .

[17]  G. Tang,et al.  Optimal sliding mode control for linear time-delay systems with sinusoidal disturbances , 2007 .

[18]  Yuanqing Xia,et al.  Robust delay-dependent sliding mode control for uncertain time-delay systems , 2008 .

[19]  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.

[20]  Huijun Gao,et al.  I filtering for 2D Markovian jump systems , 2008, Autom..

[21]  Yuanqing Xia,et al.  Control for discrete singular hybrid systems , 2008, Autom..

[22]  Christopher Edwards,et al.  Static output feedback sliding mode control for time-varying delay systems with time-delayed nonlinear disturbances , 2008 .

[23]  Xingyu Wang,et al.  Robust $H_{\infty}$ Control for Nonlinear Stochastic Systems: A Sliding-Mode Approach , 2008, IEEE Transactions on Automatic Control.

[24]  Ligang Wu,et al.  Observer-based sliding mode control for a class of uncertain nonlinear neutral delay systems , 2008, J. Frankl. Inst..

[25]  P. Shi,et al.  Robust adaptive sliding mode control for uncertain delta operator systems , 2009 .

[26]  Hailong Xing,et al.  Sliding mode variable structure control for parameter uncertain stochastic systems with time-varying delay , 2009 .

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

[28]  El Kebir Boukas,et al.  A singular system approach to robust sliding mode control for uncertain Markov jump systems , 2009, Autom..

[29]  Yuanqing Xia,et al.  Stability and stabilization of continuous-time singular hybrid systems , 2009, Autom..

[30]  James Lam,et al.  Robust H∞ dynamic output feedback control for 2D linear parameter-varying systems , 2009, IMA J. Math. Control. Inf..

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

[32]  Yuanqing Xia,et al.  Adaptive Backstepping Controller Design for Stochastic Jump Systems , 2009, IEEE Transactions on Automatic Control.

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

[34]  Michael V. Basin,et al.  Sliding mode regulator as solution to optimal control problem for nonlinear polynomial systems , 2009, 2009 American Control Conference.

[35]  Lixian Zhang,et al.  H∞ estimation for discrete-time piecewise homogeneous Markov jump linear systems , 2009, Autom..

[36]  Georgi M. Dimirovski,et al.  Robust H ∞ sliding mode control for a class of uncertain switched delay systems , 2009, Int. J. Syst. Sci..

[37]  Peng Shi,et al.  A mode-dependent stability criterion for delayed discrete-time stochastic neural networks with Markovian jumping parameters , 2010, Neurocomputing.

[38]  Alan S. I. Zinober,et al.  ℋ︁∞ sliding mode observers for uncertain nonlinear Lipschitz systems with fault estimation synthesis , 2010 .

[39]  Michael V. Basin,et al.  Sliding mode controller design for linear systems with unmeasured states , 2010, 2010 11th International Workshop on Variable Structure Systems (VSS).

[40]  Zhengzhi Han,et al.  H∞ non-fragile observer-based sliding mode control for uncertain time-delay systems , 2010, J. Frankl. Inst..

[41]  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.

[42]  Peng Shi,et al.  Delay‐dependent robust H∞ control for uncertain stochastic time‐delay systems , 2010 .

[43]  Xuerong Mao,et al.  SMC design for robust H∞ control of uncertain stochastic delay systems , 2010, Autom..

[44]  Huijun Gao,et al.  State Estimation and Sliding-Mode Control of Markovian Jump Singular Systems , 2010, IEEE Transactions on Automatic Control.

[45]  Daniel W. C. Ho,et al.  Sliding mode control of switched hybrid systems with stochastic perturbation , 2011, Syst. Control. Lett..

[46]  Ligang Wu,et al.  Quasi Sliding Mode Control of Differential Linear Repetitive Processes With Unknown Input Disturbance , 2011, IEEE Transactions on Industrial Electronics.

[47]  Ligang Wu,et al.  Mixed H2/H∞ approach to fault detection of discrete linear repetitive processes , 2011, J. Frankl. Inst..

[48]  Bo Meng,et al.  Dynamic soft variable structure control for singular systems , 2011, Proceedings of the 30th Chinese Control Conference.

[49]  Peng Shi,et al.  Fault-Tolerant Control for Nonlinear Markovian Jump Systems via Proportional and Derivative Sliding Mode Observer Technique , 2011, IEEE Transactions on Circuits and Systems I: Regular Papers.

[50]  Yugang Niu,et al.  Output feedback control for stochastic Markovian jumping systems via sliding mode design , 2011 .

[51]  Peng Shi,et al.  l2-l∞ filter design for discrete-time singular Markovian jump systems with time-varying delays , 2011, Inf. Sci..

[52]  Huijun Gao,et al.  Network-based feedback control for systems with mixed delays based on quantization and dropout compensation , 2011, Autom..

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

[54]  Zidong Wang,et al.  Robust ℋ︁∞ sliding mode control for nonlinear stochastic systems with multiple data packet losses , 2012 .

[55]  Shengyuan Xu,et al.  Sliding mode observer–controller design for uncertain Markovian jump systems with time delays , 2012 .

[56]  Yongduan Song,et al.  ${\cal H}_{\infty}$ Model Reduction of Takagi–Sugeno Fuzzy Stochastic Systems , 2012, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[57]  Ligang Wu,et al.  Sliding mode control with bounded L2 gain performance of Markovian jump singular time-delay systems , 2012, Autom..

[58]  Yuanqing Xia,et al.  Sliding mode attitude tracking of rigid spacecraft with disturbances , 2012, J. Frankl. Inst..

[59]  Antonella Ferrara,et al.  Sliding mode optimal control for linear systems , 2012, J. Frankl. Inst..

[60]  Yonggui Kao,et al.  Delay-dependent robust exponential stability of Markovian jumping reaction-diffusion Cohen-Grossberg neural networks with mixed delays , 2012, J. Frankl. Inst..

[61]  Michael V. Basin,et al.  Sliding mode filter design for nonlinear polynomial systems with unmeasured states , 2012, Inf. Sci..

[62]  H. Su,et al.  Chattering Free Sliding Mode Control for Uncertain Discrete Time‐Delay Singular Systems , 2013 .

[63]  Yonggui Kao,et al.  Delay-independent sliding mode control for a class of quasi-linear parabolic distributed parameter systems with time-varying delay , 2013, J. Frankl. Inst..

[64]  Luis Gracia,et al.  Integrated sliding-mode algorithms in robot tracking applications , 2013 .