Constrained control of uncertain systems with unbounded delays

Considered in this paper is the problem of constrained control for uncertain systems with delays. The system matrices are confined by two constant matrices serving as the lower and upper bounds, respectively. The delays may be time-varying even unbounded, the unique requirement imposed on them is they should be nonnegative. When designing controller, two constraints are considered: 1). The corresponding closed-loop systems are positive. A system is said to be positive if its states and outputs are always nonnegative whenever so are its initial condition and inputs. 2). The states and inputs are bounded by a prescribed boundary, provided that the initial condition is bounded by the same boundary. A necessary and sufficient condition is established, determining whether or not such a controller exists. An numerical example is provided to illustrate the theoretical results.