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A methodology is proposed that allows for algorithmic construction of Lyapunov functions for problems concerning the stability of an equilibrium with respect to part of the variables. This methodology utilizes the previously developed sum of squares technique to determine Lyapunov certificates. Conditions for stability with respect to part of the variables are developed that allow for Lyapunov functions...
Rendezvous problems belong to the class of consensus problems where it is desired that vehicles arrive at a desired position simultaneously. Recently, the problem of rendezvous has been addressed considerably in the graph theoretic framework, which is strongly based on the communication aspects of the problem. Stability is analyzed with respect to communication topology. The current methods do not...
In this paper, we present a dynamical systems representation for multi-agent rendezvous on the phase plane. We restrict our attention to two agents, each with scalar dynamics. The problem of rendezvous is cast as a stabilization problem, with a set of constraints on the trajectories of the agents, defined on the phase plane. We also describe a method to generate control Lyapunov functions that when...
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