On distributed high-gain adaptive stabilization

In this paper we consider adaptive distributed stabilization for uncertain multivariable linear systems with a time-varying diagonal matrix gain. We show that an unknown system matrix being an M-matrix is a sufficient condition to ensure uncertain linear systems to be stabilizable by matrix high gains, and derive a threshold condition to ensure exponential stability of uncertain linear systems stabilized by a monotonically increasing diagonal gain matrix. When each individual gain function in the matrix gain is updated by state-dependent functions, the boundedness and convergence of both system states and adaptive matrix gains are guaranteed. We apply the matrix gain stabilization approach to adaptive synchronization control for complex networks with time-varying coupling weights.