Strict positive realness for linear time-delay systems

Abstract

The strict positive realness (SPR) of a linear time-delay system via a linear matrix inequality (LMI) technique is studied. Presented are sufficient conditions via LMIs such that the linear delayed system is strictly positive real. More generally, we present a memoryless state feedback controller via LMIs such that the resulting closed-loop system is SPR with an α -asymptotic stability constraint (α -SPR) for a class of linear time-delay control systems. Furthermore, an LMI approach to the optimization problem of computation of the maximal allowable bound on the time delays is given such that the closed-loop system is α -SPR. Finally, a numerical example illustrates the effectiveness of the results.