Transactions of the Institute of Systems, Control and Information Engineers
Online ISSN : 2185-811X
Print ISSN : 1342-5668
Analysis of Nonlinear Systems in Specified Regions of the State Space by Using Density Functions Characterizing Positively Invariant Sets
Izumi MASUBUCHI
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2006 Volume 19 Issue 12 Pages 453-461

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Abstract

This paper is concerned with analysis of positive invariance and regional almost convergence of nonlinear systems by using density functions. It is shown that 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 are convergent. This result is applicable to controller synthesis for nonlinear systems by using convex optimization with satisfying state and input constraints. Furthermore, converse theorems are provided to ensure the existence of such density functions under mild assumptions.

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