Impulsive observers with variable update intervals for Lipschitz nonlinear time-delay systems

This article is concerned with the design of impulsive observers with variable update intervals for Lipschitz nonlinear systems with delays in state. Discontinuous Lyapunov function/funtional approaches are developed to analyse the stability of error dynamics. Delay-independent sufficient conditions for uniform exponential stability of the error dynamics over variable update intervals are derived in terms of linear matrix inequalities (LMIs). When these LMIs are feasible, the observer gain matrix can be solved numerically with an LMI-based optimisation algorithm. Numerical examples are provided to show the efficiency of the proposed approach.