Lyapunov Design of Cooperative Control and Its Application to the Consensus Problem

In this paper, cooperative control of nonlinear networked systems is investigated. In particular, the Lyapunov direct method is applied to stability analysis and control design of cooperative systems. The proposed design is based on a necessary and sufficient condition of (linear) cooperative controllability on properties of arbitrarily time-varying topologies and on their corresponding control Lyapunov functions. A class of cooperative control Lyapunov functions with respect to the consensus set x = c1 is explicitly found, and a Lyapunov argument is presented for both analysis and design. Examples are included to illustrate both the design process and performance of cooperative controls.