H2 Controller Design for Multi-Agent Systems with Markovian Switching Topologies

This paper presents a H2 controller design method for discrete-time multi-agent systems with Markovian switching topologies using linear matrix inequalities (LMIs). The consensus problem is first reformulated as an equivalent error system, allowing for consensus error dynamics of general directed graph topologies to be considered. This error dynamic system is used in controller design, and it is shown how with appropriate constraints fundamental results from Markov jump linear systems literature may be used to design a distributed controller for the multi-agent system. Applying H2-norm control design ensures mean-square consensusability of the multi-agent system can be achieved while allowing for more intuitive controller design through selection of the performance function. Simulation results are provided to show the applicability of the proposed design method to switching general directed graphs and give an example of controller tuning with the proposed LMI problem.