Global stabilization of nonlinear systems based on vector control lyapunov functions

Details Global stabilization of nonlinear systems based on vector control lyapunov functions Global stabilization of nonlinear systems based on vector control lyapunov functions

2012-01-12

arxiv.org/abs/1201.2478v1

Mathematics

Optimization and Control

25 pages, to be submitted to IEEE Transactions on Automatic Control

Scientific paper

This paper studies the use of vector Lyapunov functions for the design of globally stabilizing feedback laws for nonlinear systems. Recent results on vector Lyapunov functions are utilized. The main result of the paper shows that the existence of a vector control Lyapunov function is a necessary and sufficient condition for the existence of a smooth globally stabilizing feedback. Applications to nonlinear systems are provided: simple and easily checkable sufficient conditions are proposed to guarantee the existence of a smooth globally stabilizing feedback law. The obtained results are applied to the problem of the stabilization of an equilibrium point of a reaction network taking place in a continuous stirred tank reactor.

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