Stability analysis of linear delay systems with cone invariance

This paper is concerned with the stability and input-output gain analysis of linear delay systems with cone invariance. Based on the partial ordering over a cone, the monotonicity of the trajectory of the cone-preserving systems with constant delays is first studied. Then, by comparing the trajectory of the constant delay systems and that of time-varying delay systems, we prove that a cone-preserving system with interval time-varying delays is asymptotically stable if and only if the corresponding delay-free system is asymptotically stable. This implies that the stability of a cone-preserving system is insensitive to the magnitude of the delays. Moreover, based on the cone-induced norms, an explicit characterization on the cone-induced gain of an input-output cone-preserving system is given in terms of system matrices. Finally, numerical examples are provided to illustrate the theoretical results.