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Neural network based finite-time stabilization for discrete-time Markov jump nonlinear systems with time delays. (English) Zbl 1291.93313

Summary: This paper deals with the finite-time stabilization problem for discrete-time Markov jump nonlinear systems with time delays and norm-bounded exogenous disturbance. The nonlinearities in different jump modes are parameterized by neural networks. Subsequently, a linear difference inclusion state space representation for a class of neural networks is established. Based on this, sufficient conditions are derived in terms of linear matrix inequalities to guarantee stochastic finite-time boundedness and stochastic finite-time stabilization of the closed-loop system. A numerical example is illustrated to verify the efficiency of the proposed technique.

MSC:

93E15 Stochastic stability in control theory
93D15 Stabilization of systems by feedback
60J20 Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.)
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