H∞ leader-following consensus of nonlinear multi-agent systems under semi-Markovian switching topologies with partially unknown transition rates

Abstract

This paper investigates the H∞ leader-following consensus problem for nonlinear multi-agent systems under semi-Markovian switching topologies. The switching of the topologies is governed by a semi-Markovian jump process, which covers a Markovian jump process as a special case. In many practical systems, it is difficult to obtain the transition rate matrix, thus the transition rates are considered to be not completely known in the paper. External perturbations are considered in the paper, and H∞ control theory is applied. By utilising stochastic technique, sufficient conditions expressed in terms of linear matrix inequalities are derived to ensure that the H∞ leader-following consensus can be reached with a prescribed performance index. Finally, a numerical example is given to show the effectiveness of the theoretical results.