Stability of Nonlinear Delayed Systems With Logically Selected Impulses

This article investigates the global exponential stability of the nonlinear delayed systems with logically selected impulses. First, the mathematical model for a new kind of hybrid systems is proposed. Based on the semi-tensor product of matrices, several sufficient conditions for globally exponential stability are derived. The impulsive switching signals are generated by two types of logical dynamical systems of addressed systems. To be specific, one signal is given in advance, and the other one is determined by some impulsive cycle sequences. An algorithm is developed to design logical dynamical systems for determining impulsive signals. The effectiveness of the main results is verified by two examples.