This chapter describes a stability and control design framework for time-varying and time-invariant sets of nonlinear dynamical systems. The framework is applied to the problem of coordination control for multiagent interconnected systems predicated on vector Lyapunov functions. In multiagent systems, several Lyapunov functions arise naturally where each agent can be associated with a generalized energy function corresponding to a component of a vector Lyapunov function. The chapter characterizes a moving formation of vehicles as a time-varying set in the state space to develop a distributed control design framework for multivehicle coordinated motion control by designing stabilizing controllers for time-varying sets of nonlinear dynamical systems. The proposed cooperative control algorithms are shown to globally exponentially stabilize both moving and static formations.
