Stability analysis for discrete-time nonlinear systems based on density functions

Abstract

Stability analysis based on density functions is a dual notion of the well-known Lyapunov's stability analysis method which is useful in designing state-feedback controllers. This paper proposes a version of this method for discrete-time nonlinear systems. Whereas the existing method for continuous-time systems is based on analyzing the divergence of the state-space flow, this paper introduces its discrete-time version which enables one to obtain a novel stability analysis method for discrete-time nonlinear systems. The main result of the paper provides a necessary and sufficient condition for asymptotic stability.