Design of state‐dependent impulsive observer for non‐linear time‐delay systems

Abstract

In this study, a new state-dependent impulsive observer (SDIO) is proposed for a class of non-linear time-delay systems. The proposed observer is based on the extended pseudo-linearisation technique that parameterises the non-linear time-delay system to a pseudo-linear structure with time delay and state-dependent coefficients. Applying this technique, the presented observer is utilised for non-linear systems with multiple, time-varying and distributed delays. Furthermore, the extended pseudo-linearisation technique simplifies the procedure of impulsive observer design for non-linear time-delay systems. The proposed SDIO is capable of continuously estimating system states using discrete samples of the system output that are available at discrete impulse times. The stability and convergence of the proposed observer are proven via a theorem utilising time-varying and delay-independent Lyapunov function and the comparison system theory of impulsive systems. It is guaranteed that the estimation error asymptotically converges to zero under well-defined and less-conservative sufficient conditions that are presented in terms of feasible linear matrix inequalities. In addition, the stability theorem specifies an upper bound on the time intervals between consecutive impulses. Results are simulated on Congo Ebola disease model which is an epidemic non-linear time-delay system. Simulation results confirm the effectiveness and performance of the proposed SDIO.