Design of Adaptive State-Dependent Impulsive Observer for Nonlinear Time-Delay Systems

In current study, a recent adaptive state-dependent impulsive observer (ASDIO) is suggested for a wider category of nonlinear dynamics with delays in states. The suggested observer is on the basis of the extended pseudo-linearization technique. By applying this technique, the presented observer is utilized for nonlinear dynamics with several, distributed, and time-varying delays. Furthermore, the extended pseudo-linearization technique simplifies the procedure of impulsive observer layout for nonlinear time-delay dynamics. The constancy and convergence of the suggested observer are proven via a theorem utilizing the comparison system theory corresponding to impulsive systems. It is assured that the estimation error shows an asymptotic convergence to zero subject to adequate terms with less conservatism that are exhibited in the form of feasible linear matrix inequalities (LMIs). In addition, the stability theorem specifies a maximum value of the impulses time. The results are applied on Congo Ebola disease model which is an epidemic nonlinear time-delay system. Simulations confirm the efficiency of the presented ASDIO.