Improved Consensus Conditions for Multi-Agent Systems With Uncertain Topology: The Generalized Transition Rates Case

This paper is dedicated to addressing the consensus issues for a class of multi-agent systems (MASs) subjected to Markovian switching interaction topology and time-varying input delay. In line with this consideration, we first propose a modified reciprocally convex inequality, named as delay-dependent reciprocally convex inequality to obtain a tighter upper bound about the time-derivative of Lyapunov–Krasovskii functional. As a result, an improved condition with less conservatism stated elegantly in terms of linear matrix inequalities is established such that the MASs with Markovian switching topology and time varying input delay can approach the unified state. Further, the general cases of Markovian switching topology where each transition rate is completely unknown or just its estimate value is known are systematically investigated as well. Moreover, to make our results more meaningful, several comparison results concerning the admissible input delay against other related ones are also presented, which yield that our consensus conditions significantly improve the existing ones advocated thus far. Finally, we verify the validity, the effectiveness, and the practical applicability of our results in the simulation examples.