Uniform semistability for time-varying dynamical systems and network consensus with time-dependent communication links

This paper focuses on uniform semistability and uniform finite-time semistability for time-varying dynamical systems. Semistability is the property whereby the solutions of a dynamical system converge to Lyapunov stable equilibrium points determined by the system initial conditions. Using these results we develop a framework for designing semistable protocols in dynamical networks with time-dependent communication links. Specifically, we present distributed nonlinear time-varying control architectures for multiagent network consensus with dynamic communication links.