Fixed-Order Decentralized Dynamic Output Feedback Controller Design for Consensus of Multi-Agent Systems with Time Delay

This paper presents a novel delay-dependent consensus algorithm within the linear matrix inequality (LMI) framework to solve consensus problem of linear multi-agent systems with time-varying communication and input delays using fixed-order dynamic output feedback controller. The proposed scheme is decentralized in the sense that each agent updates its state according to the output information of itself and its neighbors. To guarantee consensus in this method, first based on graph theory and by proper system transformations, the consensus problem is converted to the stability problem of an equivalent state-delayed linear system. Then, by considering a suitable Lyapunov-Krasovskii function and applying special conditions on symmetric positive definite matrices, new delay-dependent consensus criteria in LMI form and the unknown controller coefficients are obtained for the system under fixed interconnection topology which can be easily solved by various effective optimization algorithms. As a main feature of the proposed approach, the order of decentralized controllers can be chosen arbitrarily according to the system conditions and limitations. Finally, a numerical example is presented to show the applicability and effectiveness of the proposed method.