Stability of bimodal planar linear switched systems

TL;DR

This paper derives dwell time bounds for bimodal planar switched linear systems, ensuring their asymptotic stability, by analyzing eigenstructure and optimizing eigenvector scaling, with comparisons to existing bounds.

Contribution

It introduces a novel method to compute smooth dwell time bounds based on eigenvector scaling for bimodal planar systems, improving stability guarantees.

Findings

Derived explicit dwell time bounds as smooth functions of eigenvectors and eigenvalues.

Optimized eigenvector scaling to strengthen stability bounds.

Compared new bounds with existing literature, demonstrating improvements.

Abstract

We consider bimodal planar switched linear systems and obtain dwell time bounds which guarantee their asymptotic stability. The dwell time bound obtained is a smooth function of the eigenvectors and eigenvalues of the subsystem matrices. An optimal scaling of the eigenvectors is used to strengthen the dwell time bound. A comparison of our bounds with the dwell time bounds in the existing literature is also presented.