Masubuchi, Izumi (Hiroshima Univ.)

Characterization of Positively Invariant Sets by Density Functions

Scheduled for presentation during the Regular Session "Stability I" (WeA13), Wednesday, July 26, 2006, 10:25−10:50, Room 101

17th International Symposium on Mathematical Theory of Networks and Systems, July 24-28, 2006, Kyoto, Japan

This information is tentative and subject to change. Compiled on April 26, 2024

Abstract

This paper is concerned with analysis of positive invariance and almost convergence of trajectories of nonlinear systems by using density functions. If there exists a density function that is positive inside a set and zero on its boundary then the set is positively invariant and almost all of the trajectories starting from the set converge to the equilibrium point. This is applicable to controller synthesis for nonlinear systems by using convex optimization with satisfying state and input constraints. Converse theorems are provided to ensure the existence of such density functions.