Stability Analysis of Hybrid Integrator-Gain Systems using Linear Programming

Juan Javier Palacios Roman; Sigurdur F. Hafstein; Sebastiaan J.A.M. van den Eijnden; Marcel F. Heertjes; W. P.M.H. Heemels

doi:10.1016/j.ifacol.2024.07.419

Stability Analysis of Hybrid Integrator-Gain Systems using Linear Programming

Juan Javier Palacios Roman (Corresponding author), Sigurdur F. Hafstein, Sebastiaan J.A.M. van den Eijnden, Marcel F. Heertjes, W. P.M.H. Heemels

Research output: Contribution to journal › Conference article › peer-review

1 Citation (Scopus)

Abstract

Stability and performance of hybrid integrator-gain systems (HIGS) are mostly analyzed using linear matrix inequalities (LMIs) to construct continuous piecewise quadratic (CPQ) Lyapunov functions. To create additional methods for the analysis of HIGS and other conewise linear systems, a method based on linear programming (LP) for constructing continuous piecewise affine (CPA) Lyapunov functions is investigated. In this paper, it is shown how linear programming can be used to prove input-to-state stability and calculate upper bounds on the L1-gain and H1-norm. The numerical efficiency of this CPA (LP) method will be compared to that of the CPQ (LMI) method on a numerical example involving HIGS.

Original language	English
Pages (from-to)	19-24
Number of pages	6
Journal	IFAC-PapersOnLine
Volume	58
Issue number	11
DOIs	https://doi.org/10.1016/j.ifacol.2024.07.419
Publication status	Published - 1 Jul 2024
Event	8th IFAC Conference on Analysis and Design of Hybrid Systems, ADHS 2024 - Boulder, United States Duration: 1 Jul 2024 → 3 Jul 2024

Bibliographical note

Publisher Copyright:
© 2024 The Authors. This is an open access article under the CC BY-NC-ND license.

Keywords

input-to-state stability
linear programming
Lyapunov methods
performance analysis
stability of hybrid systems

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title = "Stability Analysis of Hybrid Integrator-Gain Systems using Linear Programming",

abstract = "Stability and performance of hybrid integrator-gain systems (HIGS) are mostly analyzed using linear matrix inequalities (LMIs) to construct continuous piecewise quadratic (CPQ) Lyapunov functions. To create additional methods for the analysis of HIGS and other conewise linear systems, a method based on linear programming (LP) for constructing continuous piecewise affine (CPA) Lyapunov functions is investigated. In this paper, it is shown how linear programming can be used to prove input-to-state stability and calculate upper bounds on the L1-gain and H1-norm. The numerical efficiency of this CPA (LP) method will be compared to that of the CPQ (LMI) method on a numerical example involving HIGS.",

keywords = "input-to-state stability, linear programming, Lyapunov methods, performance analysis, stability of hybrid systems",

author = "{Palacios Roman}, {Juan Javier} and Hafstein, {Sigurdur F.} and {van den Eijnden}, {Sebastiaan J.A.M.} and Heertjes, {Marcel F.} and Heemels, {W. P.M.H.}",

note = "Publisher Copyright: {\textcopyright} 2024 The Authors. This is an open access article under the CC BY-NC-ND license.; 8th IFAC Conference on Analysis and Design of Hybrid Systems, ADHS 2024 ; Conference date: 01-07-2024 Through 03-07-2024",

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T1 - Stability Analysis of Hybrid Integrator-Gain Systems using Linear Programming

AU - Palacios Roman, Juan Javier

AU - Hafstein, Sigurdur F.

AU - van den Eijnden, Sebastiaan J.A.M.

AU - Heertjes, Marcel F.

AU - Heemels, W. P.M.H.

PY - 2024/7/1

Y1 - 2024/7/1

N2 - Stability and performance of hybrid integrator-gain systems (HIGS) are mostly analyzed using linear matrix inequalities (LMIs) to construct continuous piecewise quadratic (CPQ) Lyapunov functions. To create additional methods for the analysis of HIGS and other conewise linear systems, a method based on linear programming (LP) for constructing continuous piecewise affine (CPA) Lyapunov functions is investigated. In this paper, it is shown how linear programming can be used to prove input-to-state stability and calculate upper bounds on the L1-gain and H1-norm. The numerical efficiency of this CPA (LP) method will be compared to that of the CPQ (LMI) method on a numerical example involving HIGS.

AB - Stability and performance of hybrid integrator-gain systems (HIGS) are mostly analyzed using linear matrix inequalities (LMIs) to construct continuous piecewise quadratic (CPQ) Lyapunov functions. To create additional methods for the analysis of HIGS and other conewise linear systems, a method based on linear programming (LP) for constructing continuous piecewise affine (CPA) Lyapunov functions is investigated. In this paper, it is shown how linear programming can be used to prove input-to-state stability and calculate upper bounds on the L1-gain and H1-norm. The numerical efficiency of this CPA (LP) method will be compared to that of the CPQ (LMI) method on a numerical example involving HIGS.

KW - input-to-state stability

KW - linear programming

KW - Lyapunov methods

KW - performance analysis

KW - stability of hybrid systems

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DO - 10.1016/j.ifacol.2024.07.419

M3 - Conference article

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VL - 58

SP - 19

EP - 24

JO - IFAC-PapersOnLine

JF - IFAC-PapersOnLine

IS - 11

T2 - 8th IFAC Conference on Analysis and Design of Hybrid Systems, ADHS 2024

Y2 - 1 July 2024 through 3 July 2024

ER -

Stability Analysis of Hybrid Integrator-Gain Systems using Linear Programming

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Keywords

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