A stability property of nonlinear systems with inputs having slowly varying average and its application to HIV problem

In this paper, a stability property is proved for a class of three-time-scale systems, which is induced by a time-varying input that is highly oscillatory but, on average, is slowly-varying. We show a practical stability for such systems in the sense that if the ratios of time-scales are sufficiently large, the systems still remain close to the point that is an equilibrium of the average of the input. As an application, a drug dose control problem for the AIDS treatment is considered. The main result asserts that the long-term planning of drug dose is still effective under the short term variation of drug effect in a body.