Consensus of semi‐Markov multi‐agent systems with stochastically unmatched topologies

This paper addresses the consensus problem of semi‐Markov multi‐agent systems, where the topology switching is stochastically unmatched to the original switching. The unmatched property is described by a stochastically conditional probability and quantized by a given transition probability density function (PDF). Then a consensus protocol based on the aforementioned topology is proposed and includes mode‐dependent and ‐independent control inputs as special cases. Based on the Lyapunov function approach and some enlarging techniques, sufficient LMI conditions are presented to solve the controller directly. All the features such as conditional probability, dwell time and transition probability are involved. An improved method but needing nonsingular expectation of the truncated PDF matrix is also proposed. A practical example is offered so as to verify the effectiveness and superiority of the methods proposed in this study.