Characterization of Positively Invariant Sets and Almost Convergence of Trajectories of Nonlinear Systems via Density Functions

Abstract

This paper proposes a new method of regional stability analysis of nonlinear systems based on Rantzer's density functions, We show a sufficient condition in terms of density functions to guarantee positive invariance of a set and convergence of almost all trajectories therein. This condition leads to a convex formulation of synthesis with state and input constraints.