Analysis and robust [formula omitted] control for systems of stochastic differential equations with piecewise constant arguments

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This paper deals with systems of stochastic differential equations with piecewise constant arguments (SEPCA), where the arguments are of a delay type. To reduce the complexity of the proposed system, SEPCA is treated as a hybrid (or switched) system. This effective approach motivates the applicability of the classical theory of ordinary stochastic differential equations and the design of a switching law. We are mainly concerned with establishing some fundamental properties including the existence of a unique solution, mean-square (m.s.) stability and the stabilization of the system. The existence-uniqueness result is obtained under the Lipschitz condition and linear growth of the systems coefficients. Moreover, the stability property is developed by two techniques, namely the comparison principle and Razumikhin methodology in which we use the Lyapunov function rather than Lyapunov functional. To enhance these theoretical results, the problem of the input-to-state stabilization (ISS) is achieved by a robust H∞ control for systems with admissible parameter uncertainty and is subjected to time-varying disturbance input. Numerical examples with simulations are presented to clarify the proposed approaches.