Average Dwell-time Conditions for Consensus of Discrete-time Linear Multi-agent Systems with Switching Topologies and Time-varying Delays

This paper investigates the consensus problem of discrete-time linear multi-agent systems (DLMASs) with directed switching information topologies and time-varying delays. First, we transform the consensus problem to an asymptotic stability problem of a corresponding time-delayed switched linear system (TDSLS) via a proper linear transformation. Then by using a constructed Lyapunov functional and the average dwell-time scheme, we establish a novel delay-dependent sufficient condition for the solvability of the consensus problem in terms of linear matrix inequalities (LMIs) for two cases, respectively: 1) all of the given information topologies are consensusable; 2) some of the given information topologies are consensusable. Finally, numerical examples are given to show the validness of the established results.