On constructing network Lyapunov function for leaderless consensus over switching digraphs

Abstract

This paper investigates the exponential Lyapunov analysis for leaderless consensus of networks with directed switching graphs. Both discrete-time and continuous-time linear agent dynamics are considered. A quadratic Lyapunov function is constructed using two positive definite matrices. Two graph matrix inequalities are proposed using the graph Laplacian matrix to calculate the graph positive definite matrix for constructing the Lyapunov function. The continuous-time Riccati inequality and a modified discrete-time Riccati inequality are utilized to calculate the dynamics positive definite matrix for the Lyapunov function design as well as the distributed control design. Average dwell time (ADT) is used to describe the switching signal. Lyapunov analysis is performed to achieve exponential leaderless consensus with convergence rate specified by the parameters in the matrix inequalities and ADT.