# Lyapunov Function Computation for Linear Switched Systems: Comparison of SDP and LP Approaches

### Stefania Andersen, Elias August, Sigurdur Hafstein, Jacopo Piccini

#### 2023

#### Abstract

For a switched system, of which each subsystem is linear, the exponential stability of the origin is equivalent to the existence of a common Lyapunov function (CLF) for all the subsystems. A popular approach to search for the latter is by means of solving a linear matrix inequality (LMI) using semidefinite programming (SDP). Another approach is to use linear programming (LP). The contribution of this work is twofold. First, we compare the SDP approach to the LP approach, with and without a certain preconditioning of system matrices. And, second, we present a software tool to visualise the conditions for a CLF. As the problem of investigating the stability of the origin is a very difficult one and sufficient and necessary conditions using the system matrices are only known for exponential stability of planar systems, a tool to visualise the original data in some meaningful form is potentially of great use for the full understanding of the problem.

Download#### Paper Citation

#### in Harvard Style

Andersen S., August E., Hafstein S. and Piccini J. (2023). **Lyapunov Function Computation for Linear Switched Systems: Comparison of SDP and LP Approaches**. In *Proceedings of the 13th International Conference on Simulation and Modeling Methodologies, Technologies and Applications - Volume 1: SIMULTECH*; ISBN 978-989-758-668-2, SciTePress, pages 61-70. DOI: 10.5220/0012084100003546

#### in Bibtex Style

@conference{simultech23,

author={Stefania Andersen and Elias August and Sigurdur Hafstein and Jacopo Piccini},

title={Lyapunov Function Computation for Linear Switched Systems: Comparison of SDP and LP Approaches},

booktitle={Proceedings of the 13th International Conference on Simulation and Modeling Methodologies, Technologies and Applications - Volume 1: SIMULTECH},

year={2023},

pages={61-70},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0012084100003546},

isbn={978-989-758-668-2},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 13th International Conference on Simulation and Modeling Methodologies, Technologies and Applications - Volume 1: SIMULTECH

TI - Lyapunov Function Computation for Linear Switched Systems: Comparison of SDP and LP Approaches

SN - 978-989-758-668-2

AU - Andersen S.

AU - August E.

AU - Hafstein S.

AU - Piccini J.

PY - 2023

SP - 61

EP - 70

DO - 10.5220/0012084100003546

PB - SciTePress