A Linear Program to Compare Path-Complete Lyapunov Functions

David  Angeli; Nikolaos Athanasopoulos; Raphael M. Jungers; Matthew Philippe

doi:10.1109/CDC.2017.8264550

A Linear Program to Compare Path-Complete Lyapunov Functions

David Angeli, Nikolaos Athanasopoulos, Raphael M. Jungers, Matthew Philippe

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

3 Citations (Scopus)

359 Downloads (Pure)

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.

Original language	English
Title of host publication	IEEE 56th Annual Conference on Decision and Control 12-15 Dec. 2017
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	5888-5893
Number of pages	6
ISBN (Electronic)	978-1-5090-2873-3
DOIs	https://doi.org/10.1109/CDC.2017.8264550
Publication status	Published - 23 Jan 2018

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A Linear Program to Compare Path-Complete Lyapunov Functions
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Cite this

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title = "A Linear Program to Compare Path-Complete Lyapunov Functions",

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 impliesexistence 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.",

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AU - Philippe, Matthew

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N2 - 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 impliesexistence 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.

AB - 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 impliesexistence 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.

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DO - 10.1109/CDC.2017.8264550

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BT - IEEE 56th Annual Conference on Decision and Control 12-15 Dec. 2017

PB - Institute of Electrical and Electronics Engineers Inc.

ER -

A Linear Program to Compare Path-Complete Lyapunov Functions

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