Summary

2011 International Symposium on Nonlinear Theory and Its Applications

2011

Session Number:C3L-D

Session:

Number:C3L-D1

Density Functions for Analysis of Positive Invariance and Convergence of Trajectories for Nonlinear Systems with a Piecewise-C2 Vector Field

Izumi Masubuchi,  

pp.701-704

Publication Date:2011/9/4

Online ISSN:2188-5079

DOI:10.34385/proc.45.C3L-D1

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Summary:
This paper considers positive invariance and convergence of trajectories of nonlinear systems via Rantzer’s density functions. Unlike many of previous results on density functions, this paper does not assume that the vector field of the system is continuously differentiable on the whole state space but admits vector fields that can be not differentiable in measure-zero subsets. Under mild assumptions, a criterion is proposed to guarantee that a given open set is positively invariant and almost all of the trajectories starting from the set converge to a relevant equilibrium in the set.