Non-fragile consensus control for singular multi-agent systems with Lipschitz nonlinear dynamics

Abstract

In this paper, the problem of non-fragile consensus control for continuous-time singular multi-agent systems with respect to Lipschitz nonlinear dynamics is investigated. Considerations are that the concerned nonlinear singular dynamical agents communicate in an undirected connected topology and the states of all agents achieve consensus by the designed protocol which is subject to norm-bounded parametric uncertainty. On the basis of nonsingular transformation, non-fragile consensus performance analysis for the concerned multi-agent systems is converted into asymptotical stabilization problems of some lower dimensional subsystems. By exploiting the structure of the nonsingular transformation matrix, moreover, the impacts of the Lipschitz nonlinear dynamics are eliminated. Benefitting from the introduced free-weighting matrices, sufficient conditions for non-fragile consensus controller design are formulated in terms of linear matrix inequalities. Furthermore, the explicit dynamical expression and the determined initial states of the consensus function are also given. Numerical examples are exploited to illustrate effectiveness of the derived results.