Gain‐scheduled robust control for multi‐agent linear parameter‐varying systems with communication delays

Abstract

AbstractThis study deals with the problem of gain‐scheduled robust control for multi‐agent linear parameter varying (LPV) systems with or without communication delays. The system matrices are assumed to depend on the scheduling parameters, which are supposed to be time‐varying within a priori known bounds. First, a linear transformation matrix is constructed from the directed spanning tree of the communication topology of the agents, which equivalently transforms the robust consensus control problem of multi‐agent LPV systems into the robust stability problem of a set of parameter‐dependent systems. What's more, the effect of the time‐varying communication delays is considered, and consensus condition in terms of linear matrix inequalities (LMIs) is derived by using the parameter‐dependent Lyapunov–Krasovskii approach. Then, the control gain matrices are obtained through solving a convex optimization problem. Finally, a numerical example is provided to illustrate the effectiveness of the proposed method.