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A Linear Program to Compare Path-Complete Lyapunov Functions
File | Description | Size | Format | |
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CDC2017-AngeAthanJungPhilA_LP_To_Compare_PCLFs.pdf | Accepted version | 624.96 kB | Adobe PDF | View/Open |
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 |