Reachable Set Estimation of Multi-agent Systems under Semi-Markov Switching Topology with Partially Unknown Rates

This paper investigates the problem of error reachable set estimation for leader-follower systems under semi-Markov switching topology with partially unknown rates. The topology switching is controlled by a semi-Markov jump process. It is difficult to find the transition rates matrix completely in many practical systems so that we come to a conclusion that the transition rates is incompletely known. In this paper, we take the external perturbation problem and nonlinearity into account. By using the stochastic theory and the reachable set theory, we derive the sufficient conditions for the use of linear matrix inequalities to ensure that the error trajectory can be constrained in a given closed space under a given performance index. Finally, an example is given to verify the effectiveness of the theoretical results