Energy-to-peak consensus for multi-agent systems with stochastic disturbances and Markovian switching topologies

This paper is concerned with the problem of energy-to-peak consensus for a class of multi-agent systems with both stochastic disturbances and Markovian switching topologies. The objective is to design a control protocol in the form of dynamic output feedback, such that the multi-agent system reaches mean square consensus and has a prescribed energy-to-peak disturbance attenuation level. By using linear transformations, the problem is transformed into a standard energy-to-peak control problem. Then a new bounded real lemma is established. On the basis of this, an approach for the design of the control protocol is developed, by which the desired gain can be obtained via solving a number of linear matrix inequalities. Finally, a numerical example is provided to illustrate the effectiveness of the proposed approach.