Analyzing the effect of output measurements interval and impulses distance of an impulsive observer on the control system of HIV

Extended state-dependent Riccati equation (ESDRE) control system based on a state-dependent impulsive observer is developed for HIV, as a nonlinear time-delay system. The state-dependent impulsive observer takes measured outputs at discrete moments and uses those to estimate state of the system, continuously. The estimated values of state variables are used in control ESDRE control strategy. The impulses- distance is chosen with respect to the patient physical limitations. A time-varying Lyapunov function and comparison system theory of impulsive differential equation systems are used to prove the stability of this observer, since the observer and the controller are independent, another Lyapunov function can be used to guaranty the asymptotic stability of the closed-loop control system. Simulation results are provided to show the efficiency of the output measurements- interval and impulses distance of an impulsive observer on the control and estimation of the HIV time-delay model.