Robust stabilisation of 2D state-delayed stochastic systems with randomly occurring uncertainties and nonlinearities

This paper is concerned with the state feedback control problem for a class of two-dimensional (2D) discrete-time stochastic systems with time-delays, randomly occurring uncertainties and nonlinearities. Both the sector-like nonlinearities and the norm-bounded uncertainties enter into the system in random ways, and such randomly occurring uncertainties and nonlinearities obey certain mutually uncorrelated Bernoulli random binary distribution laws. Sufficient computationally tractable linear matrix inequality–based conditions are established for the 2D nonlinear stochastic time-delay systems to be asymptotically stable in the mean-square sense, and then the explicit expression of the desired controller gains is derived. An illustrative example is provided to show the usefulness and effectiveness of the proposed method.

[1]  Yisha Liu,et al.  Reliable H∞ filtering for discrete time-delay systems with randomly occurred nonlinearities via delay-partitioning method , 2011, Signal Process..

[2]  Fuwen Yang,et al.  Robust mixed H-2/H∞ control for a class of nonlinear stochastic systems , 2006 .

[3]  Zidong Wang,et al.  Exponential synchronization of stochastic delayed discrete-time complex networks , 2008 .

[4]  Shengyuan Xu,et al.  Stability and Stabilization of Uncertain 2-D Discrete Systems with Stochastic Perturbation , 2005, Multidimens. Syst. Signal Process..

[5]  Huijun Gao,et al.  Robust H∞ Filtering for 2D Stochastic Systems , 2004 .

[6]  Shengyuan Xu,et al.  Robust stability and stabilisation of 2D discrete state-delayed systems , 2004, Syst. Control. Lett..

[7]  T. Kaczorek.  Two-Dimensional Linear Systems , 1985 .

[8]  Jinde Cao,et al.  Global Synchronization of Linearly Hybrid Coupled Networks with Time-Varying Delay , 2008, SIAM J. Appl. Dyn. Syst..

[9]  Shengyuan Xu,et al.  Improved delay-dependent stability criteria for time-delay systems , 2005, IEEE Transactions on Automatic Control.

[10]  T. Hinamoto.  Stability of 2-D discrete systems described by the Fornasini-Marchesini second model , 1997 .

[11]  Z. Y. Gao,et al.  Stabilizabiltty of certain stochastic systems , 1986 .

[12]  T. Morozan,et al.  Optimal stabilizing compensator for linear systems with state-dependent noise , 1992 .

[13]  D. Hinrichsen,et al.  H∞-type control for discrete-time stochastic systems , 1999 .

[14]  Ting Wang,et al.  Delay-derivative-dependent stability criterion for neural networks with probabilistic time-varying delay , 2013, Int. J. Syst. Sci..

[15]  Jun Hu,et al.  Robust Sliding Mode Control for Discrete Stochastic Systems With Mixed Time Delays, Randomly Occurring Uncertainties, and Randomly Occurring Nonlinearities , 2012, IEEE Transactions on Industrial Electronics.

[16]  Huajing Fang,et al.  Fault detection for discrete-time networked nonlinear systems with incomplete measurements , 2013, Int. J. Syst. Sci..

[17]  J. Lam,et al.  IMPROVED CONDITIONS FOR DELAY‐DEPENDENT ROBUST STABILITY AND STABILIZATION OF UNCERTAIN DISCRETE TIME‐DELAY SYSTEMS , 2005 .

[18]  Yurong Liu,et al.  A note on control of a class of discrete-time stochastic systems with distributed delays and nonlinear disturbances , 2010, Autom..

[19]  Peng Shi,et al.  Stability and Stabilization , 2016 .

[20]  Zidong Wang,et al.  Robust state estimation for two-dimensional stochastic time-delay systems with missing measurements and sensor saturation , 2014, Multidimens. Syst. Signal Process..

[21]  Fuwen Yang,et al.  Robust Filtering for Systems with Stochastic Non-Linearities and Deterministic Uncertainties , 2006 .

[22]  Qing-Guo Wang,et al.  Delay-range-dependent stability for systems with time-varying delay , 2007, Autom..

[23]  Li Yu,et al.  H ∞ Control of 2-D Discrete State Delay Systems , 2006 .

[24]  Amit Dhawan.  Non-Fragile Controller Design for 2-D Discrete Uncertain Systems Described by the Roesser Model , 2012 .

[25]  Bo Shen,et al.  Robust Hinfinity finite-horizon filtering with randomly occurred nonlinearities and quantization effects , 2010, Autom..

[26]  Zidong Wang,et al.  H∞ filtering for uncertain stochastic time-delay systems with sector-bounded nonlinearities , 2008, Autom..

[27]  Shyh-Feng Chen,et al.  Delay-dependent stability for 2-D systems with delays in the Roesser model , 2010, Proceedings of the 2010 American Control Conference.

[28]  Krzysztof Galkowski,et al.  Stability and stabilization of systems modeled by 2D nonlinear stochastic roesser models , 2011, The 2011 International Workshop on Multidimensional (nD) Systems.

[29]  Zidong Wang,et al.  A delay fractioning approach to global synchronization of delayed complex networks with stochastic disturbances , 2008 .

[30]  Lihua Xie,et al.  Output feedback H∞ control of systems with parameter uncertainty , 1996 .

[31]  Shuxia Ye,et al.  Robust stabilization of 2-D state-delayed systems with stochastic perturbation , 2010, 2010 11th International Conference on Control Automation Robotics & Vision.

[32]  Zidong Wang,et al.  Global synchronization for delayed complex networks with randomly occurring nonlinearities and multiple stochastic disturbances , 2009 .

[33]  Zidong Wang,et al.  Probability‐dependent gain‐scheduled control for discrete stochastic delayed systems with randomly occurring nonlinearities , 2013 .

[34]  Mauro Bisiacco.  New results in 2D optimal control theory , 1995, Multidimens. Syst. Signal Process..

[35]  Z. Gao,et al.  Feedback stabilizability of non-linear stochastic systems with state-dependent noise , 1987 .

[36]  Zhengrong Xiang,et al.  Delay-dependent robust $$H_\infty $$ control for 2-D discrete nonlinear systems with state delays , 2014, Multidimens. Syst. Signal Process..

[37]  G. Marchesini,et al.  State-space realization theory of two-dimensional filters , 1976 .

[38]  Shengyuan Xu,et al.  Robust H∞ control for a class of uncertain nonlinear two-dimensional systems with state delays , 2005, J. Frankl. Inst..