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This article addresses a class of large-scale stochastic impulsive systems with time delay and time-varying input disturbance having bounded magnitude. The main interest is to develop sufficient conditions for the input-to-state stability (ISS) and stabilization in the presence of impulsive effects. The method of Razumikhin–Lyapunov function is used to develop the ISS and stabilization properties. Later, these results are applied to a class of control systems where the controller actuators are susceptible to failures. It should be noted that our results are delay independent, and the designed reliable controller is robust with respect to the actuator failures and to the system uncertainties. It is also observed that if the isolated continuous system is ISS and subjected to bounded impulsive effects, then the resulting impulsive system preserves the ISS property. Moreover, if the isolated continuous subsystems are all ISS and the interconnection amongst them is bounded from above, then the impulsive interconnected system is ISS provided that the degree of stability of each subsystem is larger than the magnitude of interconnection. If the underlying continuous system is unstable, then the input-to-state stabilization of the impulsive system is guaranteed if the stabilizing impulses are applied to the system frequently. As an implication to these results, if the input disturbance is zero, then the input-to-state stability (or stabilization) reduces to the stability (or stabilization) of the equilibrium state of the underlying disturbance-free system. A numerical example and simulations are provided to illustrate the proposed results. [ABSTRACT FROM AUTHOR]

This article establishes mean square stability and stabilization for stochastic delay systems with impulses. Using Razumikhin methodology, two approaches, classical Lyapunov-based method and comparison principle, are proposed to develop sufficient conditions that guarantee the stability and stabilization properties. It is shown that if the continuous system is stable and the impulses are destabilizing, the impulses should not be applied frequently. On the other hand, if the continuous system is unstable, but the impulses are stabilizing, the impulses should occur frequently to compensate the continuous state growth. Numerical examples are also presented to clarify the proposed theoretical results. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of designing a robust reliable H∞ control and a switching law to guarantee input-to-state stabilization (ISS) for a class of uncertain switched control systems with time delay not only when all the actuators are operational, but also when some of them experience failure. The output of faulty actuators are treated as a disturbance signal that is augmented with the system disturbance input. Multiple Lyapunov function with Razumikhin technique, and average dwell-time switching signal are used to establish the ISS property. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]