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

Zhaoxia Duan, Zhengrong Xiang and Hamid Reza Karimi

International Journal of Systems Science, 2014, vol. 45, issue 7, 1402-1415

Abstract: 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.

Date: 2014
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DOI: 10.1080/00207721.2013.835004

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