Strict positive realness for linear time-invariant systems with time-delays

Strict positive realness (SPR) of linear time-invariant systems with multiple time-delays is discussed. We present sufficient conditions via linear matrix inequalities (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 α-asymptotic stability constraint (α-SPR) for a class of linear time-delay control system. Furthermore, we give an LMI approach to the optimization problem of computation of the maximal allowable bound on the time-delays such that the closed-loop system is α-SPR