Semi-time-varying H ∞ controller for SLPV systems with modal persistent dwell time

This paper is concerned with the stability, l 2 -gain analysis and H ∞ control for a class of discrete-time switched linear parameter-varying (SLPV) systems with modal persistent dwell time (MPDT) switching. The proposed switching law is more general covering the dwell-time (DT) and average dwell-time (ADT) switching as a special case. By invoking a novel semi-time-varying (STV) multiple Lyapunov-like function, the stability criterion for the systems under MPDT switching in nonlinear settings is established as a first attempt, upon which the desired STV stabilizing controller is designed such that the SLPV system is globally uniformly asymptotically stable and has a guaranteed H ∞ noise attenuation performance. Finally, a numerical example is provided to illustrate the validity and potential of the acquired theoretical results.