H_∞ performance for a class of uncertain stochastic nonlinear Markovian jump systems with time-varying delay via adaptive control method

Abstract

This paper studies the H_∞ performance for the uncertain recurrent neural networks with both nonlinear external disturbance and Markovian jump parameters, in which the time delay is varying. Our objective is to design robust controllers, that are independent of the time delay, such that the uncertain system is stochastic stable with a generalized H_∞ disturbance attenuation level γ. For the given uncertain stochastic system, new controllers which are composed of a linear controller and an adaptive controller are proposed to realize H_∞ control by introducing a switching function and using the idea of completing square. Based on It$\hat{\text{o}}$’s differential formula and Lyapunov stability theory, new sufficient conditions are obtained in terms of linear matrices inequalities. A numerical example is constructed to show effectiveness of the designed controller in this paper.