Gain‐scheduled control for discrete‐time non‐linear parameter‐varying systems with time‐varying delays

Abstract

This study addresses the gain‐scheduled control problem for discrete‐time delayed non‐linear parameter‐varying (NLPV) and linear parameter‐varying (LPV) systems. First, by constructing the parameter‐dependent Lyapunov–Krasovskii functional and employing multiple auxiliary functions, delay‐dependent reciprocally convex inequality, and selecting a suitable augmented vector, novel delay‐dependent linear matrix inequality conditions for the static output‐feedback control design and state‐feedback control design for delayed NLPV are provided. Second, the results obtained for discrete‐time delayed NLPV systems are modified in a simple way to deal with discrete‐time delayed LPV systems. Finally, the effectiveness of the proposed methods is illustrated by numerical examples.