Stability analysis of LPV time-delayed systems

Abstract

This work provides one of the first attempts to derive computationally tractable criteria for analysing the stability of linear parameter varying (LPV) time-delayed systems. We present both delay-independent and delay-dependent stability conditions, which are derived using appropriately selected Lyapunov-Krasovskii functionals. According to the system parameter dependence, these functionals can be selected to obtain increasingly non-conservative results. Gridding techniques may be used to cast these tests as linear matrix inequalities (LMIs). In cases when the system matrices depend affinely or quadratically on the parameter, gridding may be avoided. These LMIs can be solved efficiently using available software. A numerical example of a time-delayed system motivated by a metal removal process is used to demonstrate the theoretical results.