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A Linear Program to Compare Path-Complete Lyapunov Functions

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Title: A Linear Program to Compare Path-Complete Lyapunov Functions
Authors: Angeli, D
Athanasopoulos, N
Jungers, RM
Philippe, M
Item Type: Conference Paper
Abstract: We provide an algorithmic procedure allowing to compare stability certificates for discrete-time switching systems and in specific Path-Complete Lyapunov functions (PCLFs). These mathematical objects consist of a set of positive definite functions and a set of Lyapunov inequalities, encoded in a directed, labeled graph. Given two such graphs, we formulate necessary and sufficient conditions to decide if the existence of a PCLF for the first graph implies existence of a PCLF for the second graph, where the corresponding set of functions is constructed by conic combinations of the set of functions related to the first PCLF. The conditions depend only on the topologies of the two graphs and can be verified by solving a linear program. It is the first systematic approach to compare the conservativeness of PCLFs.
Issue Date: 23-Jan-2018
Date of Acceptance: 12-Dec-2017
URI: http://hdl.handle.net/10044/1/62144
DOI: https://dx.doi.org/10.1109/CDC.2017.8264550
ISSN: 0743-1546
Publisher: IEEE
Journal / Book Title: 2017 IEEE 56TH ANNUAL CONFERENCE ON DECISION AND CONTROL (CDC)
Copyright Statement: © 2017 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
Conference Name: IEEE 56th Annual Conference on Decision and Control (CDC)
Keywords: Science & Technology
Technology
Automation & Control Systems
Engineering, Electrical & Electronic
Engineering
JOINT SPECTRAL-RADIUS
HYBRID SYSTEMS
STABILITY ANALYSIS
SWITCHED SYSTEMS
INCLUSIONS
CRITERIA
Publication Status: Published
Start Date: 2017-12-12
Finish Date: 2017-12-15
Conference Place: Melbourne, AUSTRALIA
Online Publication Date: 2018-01-23
Appears in Collections:Electrical and Electronic Engineering
Faculty of Engineering