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Global asymptotic stability of oscillations with sliding modes

Gonçalves, Jorge M. (2003) Global asymptotic stability of oscillations with sliding modes. In: Triennial world congress of the International Federation of Automatic Control. Elsevier IFAC Publications. Vol.35. No.1. Pergamon , Oxford, pp. 173-178. ISBN 9780080442242.

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This paper explores a new methodology based on quadratic surface Lyapunov functions to globally analyze oscillations with sliding modes in relay feedback systems (RFS). The method consists in efficiently construct quadratic Lyapunov functions on switching surfaces that can be used to show that impact maps, i.e., maps from one switch to the next, are contracting. This, in turn, shows that the system is globally stable. Several classes of piecewise linear systems (PLS) were previously successfully analyzed with this methodology. In this paper, we consider PLS whose trajectories switch between subsystems of different dimensions. We present and discuss distinct relaxations leading to sufficient conditions of different conservatism and computationally complexity. The results in this paper open the door to the analysis of other, more complex classes of PLS.

Item Type:Book Section
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Additional Information:© 2002 IFAC, Published by Elsevier Ltd.
Subject Keywords:Relay; Global Stability; Quadratic Surface Lyapunov Functions; Impact Maps; Lyapunov Functions
Series Name:Elsevier IFAC Publications
Issue or Number:1
Record Number:CaltechAUTHORS:20170711-083707063
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:78932
Deposited By: Ruth Sustaita
Deposited On:11 Jul 2017 22:04
Last Modified:15 Nov 2021 17:44

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