On stability analysis of discrete-time homogeneous dynamics

Mircea Lazar; Alina I. Doban; Nikolaos Athanasopoulos

doi:10.1109/ICSTCC.2013.6688976

On stability analysis of discrete-time homogeneous dynamics

Mircea Lazar, Alina I. Doban, Nikolaos Athanasopoulos

School of Electronics, Electrical Engineering and Computer Science

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

28 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 language	English
Title of host publication	17h International Conference on System Theory, Control and Computing
Publisher	Institute of Electrical and Electronics Engineers Inc.
DOIs	https://doi.org/10.1109/ICSTCC.2013.6688976
Publication status	Published - 2013

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title = "On stability analysis of discrete-time homogeneous dynamics",

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.",

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AU - Lazar, Mircea

AU - Doban, Alina I.

AU - Athanasopoulos, Nikolaos

PY - 2013

Y1 - 2013

N2 - 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.

AB - 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.

U2 - 10.1109/ICSTCC.2013.6688976

DO - 10.1109/ICSTCC.2013.6688976

M3 - Conference contribution

BT - 17h International Conference on System Theory, Control and Computing

PB - Institute of Electrical and Electronics Engineers Inc.

ER -

On stability analysis of discrete-time homogeneous dynamics

Abstract

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