Controller design for delayed systems with positive constraint

This paper addresses the issue of controller design for a class of uncertain systems with multiple delays. Each system matrix is confined by two constant matrices, and each delay may be time-varying even unbounded. The control objective is to design a family of gain matrices such that the resulted closed-loop system is not only asymptotically stable, but also positive. A system is said to be positive if its states are always nonnegative whenever its initial condition and inputs are nonnegative. A set of equivalent conditions are established, which guarantee that the closed-loop system is positive and asymptotically stable. These conditions are formulated by means of linear programming and linear matrix inequality, which can be easily verified numerically with the popular software MATLAB. An numerical example is provided to illustrate the obtained theoretical results.