Impulsive Stabilization of Systems With Control Delay

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Input delay could lead to instability of an impulsive control system. However, the problem of input delay has been seldom studied. This work addresses the fundamentally important problem in impulsive control theory. By a novel approach, we establish Lyapunov–Razumikhin-type theorems on exponential stability of stochastic impulsive delay systems. Based on our fundamental results, we develop a foundational theory for the impulsive stabilization of stochastic delay systems with input delay. Our proposed theory provides an impulsive control design method for systems with input delay and the upper bound of input delay which the designed impulsive control scheme can admit while the resulting controlled system remains exponentially stable. As future work, we present event-triggered impulsive control systems that are a natural and significant generalization of the classical impulsive control systems in the literature.