Quadratic stabilisability of multi-agent systems under switching topologies

Abstract

This paper addresses the stabilisability of multi-agent systems (MASs) under switching topologies. Necessary and/or sufficient conditions are presented in terms of graph topology. These conditions explicitly reveal how the intrinsic dynamics of the agents, the communication topology and the external control input affect stabilisability jointly. With the appropriate selection of some agents to which the external inputs are applied and the suitable design of neighbour-interaction rules via a switching topology, an MAS is proved to be stabilisable even if so is not for each of uncertain subsystem. In addition, a method is proposed to constructively design a switching rule for MASs with norm-bounded time-varying uncertainties. The switching rules designed via this method do not rely on uncertainties, and the switched MAS is quadratically stabilisable via decentralised external self-feedback for all uncertainties. With respect to applications of the stabilisability results, the formation control and the cooperative tracking control are addressed. Numerical simulations are presented to demonstrate the effectiveness of the proposed results.

Keywords:

• multi-agent systems
• quadratic stability
• formation control
• switching topology
• uncertain switched systems

Additional information

Funding

This work was in part supported by the National Science Foundation of China [grant number 61020106005], [grant number 61203374], [grant number 61375120], [grant number 61374062]; Beijing Natural Science Foundation [grant number 4142031].