Stability analysis and constrained control of positive systems with time-varying delays: A linear copositive Lyapunov-Krasovskii functional method

Abstract

This paper considers the analysis and constrained control problems of positive systems with time-varying delays. A system is a called positive system if its states keep nonnegative whenever its initial conditions and inputs are nonnegative, and the control is under positivity constraint means that the resulting closed-loop system is not only stable, but also positive. The main contribution lies in the following aspects. Firstly, based on a linear copositive Lyapunov-Krasovskii functional, some stability criteria are established for positive systems with time-varying delays. Secondly, constrained controller for a class of systems with time-varying delays is designed, which guarantees the corresponding closed-loop system is positive and asymptotically stable. © 2011 Springer-Verlag.