Stabilising control for impulsive systems

This paper is aimed at stabilising control for impulsive systems via the state feedback. Firstly, stability analysis for the closed-loop system is conducted using a Lyapunov-like functional (LLK) that is not necessarily continuous nor positive definite. Built on two subintervals of the impulsive interval being separated by the current instant, a concrete LLK is constructed by introducing multiple integrals of the state and cross terms among the integrals, the state and impulsive states. Integral equations of the impulsive system are exploited and high-order integral inequalities are taken when estimating the derivative of the LLK. New stability results with interval dwell-time, maximal dwell-time or minimal dwell-time are obtained. Secondly, based on the stability results the stabilising control problem is solved via linear matrix inequality approach. Finally, numerical examples illustrate that the stability results are less conservative and the control for impulsive systems is valid.