On stability analysis of discrete-time homogeneous dynamics

Mircea Lazar, Alina I. Doban, Nikolaos Athanasopoulos

Research output: Chapter in Book/Report/Conference proceedingConference contribution

22 Citations (Scopus)

Abstract

This paper considers the problem of stability analysis of discrete-time dynamics that are positively homogeneous of degree one. An example of a homogeneous and even continuous dynamics that is globally exponentially stable and that does not admit any λ-contractive proper C-set is presented. This motivates us to propose a natural generalization of this concept, namely, (k, λ)-contractive proper C-sets. It is proven that this simple generalization yields a non-conservative Lyapunov-type tool for stability analysis of homogeneous dynamics, namely, sublinear finite-time Lyapunov functions. Moreover, scalable and non-conservative stability tests are established for relevant classes of homogeneous dynamics.
Original languageEnglish
Title of host publication17h International Conference on System Theory, Control and Computing
Publisher IEEE
DOIs
Publication statusPublished - 2013

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