The Robust Control For Multi-Agent Coordination With Switching Topology And Time-Delay

In recent years, the research related to the multi-agent systems has received great attention. Consensus and robust control problem of the multi-agent systems play an important role in the field of control. And time delay, widely existing in the practical multi-agent systems, is often one of the main reason of causing the systems performance deterioration. so it is very necessary to study the consensus, robust control and robust controller design of the multi-agent time-delay systems. In the paper, we focus on the multi-agent time-delay switching systems. Based on the Lyapunov stability theory , control theory and linear matrix inequalities, this paper investigate the problem of the robust control for leader-following coordination with switching topology and time-delay. The main results obtained in this paper are as follows:1. The L₂ - L_∞control problem for a class of the second order multi-agent systems with time-delay and switching topology is discussed. Consider the undirected and switching network in two cases of non-delay and time-delay, based on Lyapunov functional approach and L₂ - L_∞control theory, some consensus conditions are presented and the performance index expressions are also given, which can be expressed in the form of linear matrix inequalities.2. The L₂ - L_∞control problem for a class of the multi-agent system with the directed switching and time-delay network is discussed. Based on Lyapunov method, some sufficient conditions are presented by constructing a Lyapunov matrix and using L₂ - L_∞control theory in two cases of non-delay and time-delay.3. The H∞control problem for a class of the second order multi-agent system with the directed switching and time-delay network is investigated. Based on Lyapunov approach and H∞control theory, some sufficient conditions of the consensus problem and constraint conditions of H∞performance index are presented in the form of linear matrix inequalities. As a special example, some condition are directly given in case of the undirected switching topology according to the results of the directed switching topology.