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Abstract:
Although in recent years much attention has been paid to positive systems in general, there are still many areas that are left untouched. One of these areas, is the stability analysis of positive systems under any form of uncertainty. In this book, we study three broad classes of positive systems subject to different forms of uncertainty: nonlinear, switched and time-delay positive systems. Our focus is on positive systems which are monotone. Naturally, monotonicity methods play a key role in obtaining our results. As an application of our theoretical work on positive systems, we study a class of epidemiological systems with time-varying parameters. Most of the work done so far in epidemiology has been focused on models with time-independent parameters. Based on some of the recent results in this area, we describe the epidemiological model as a switched system and present some results on stability properties of the disease-free state of the epidemiological model.
