Sub-optimal Estimation of HIV Time-delay Model using State-Dependent Impulsive Observer with Time-varying Impulse Interval: Application to Continuous-time and Impulsive Inputs

Human Immunodeficiency Virus (HIV) weakens the immune system in confronting various diseases by attacking to CD4+T cells. In modeling HIV behavior, the number of CD4+T cells is considered as the output. But, continuous-time measurement of these cells is not possible in practice, and the measurement is only available at variable intervals that are several times bigger than sampling time. In this paper, a state-dependent impulsive observer is designed for state estimation of HIV model. In order to model the HIV behavior, nonlinear time-delay differential equation is employed which considers the intracellular delay. The proposed observer is based on extended pseudo linearization technique. Even though, the number of CD4+T cells is available only in time-varying impulse intervals, this observer is capable of providing a continuous-time estimation of HIV states. It is also suitable for the continuous-time and impulsive control inputs. The asymptotic stability analysis of the suggested observer is guaranteed based on comparison principle and sector-bounded condition under some new theorems with well-defined sufficient conditions and less conservatism. Simulation and numerical results confirmed the efficiency of the proposed method despite the variable time-delays.