Stability of bimodal planar linear switched systems

Tripathi, S. N.; Agarwal, Nikita

doi:10.48550/arxiv.2109.04201

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2021

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“…A necessary and sufficient condition for stability under arbitrary switching is given in [4] for bimodal planar linear systems, and in [8] for bimodal linear systems in R 3 . In [27], we study bimodal linear switched systems, with both its subsystems stable, to find a dwell time expression as a function of eigenvalues and eigenvectors of the subsystem matrices. We obtain optimal choices of eigenvectors which result in the least dwell time.…”

Section: Introductionmentioning

confidence: 99%

Stability of Bimodal Planar Switched Linear Systems with Both Stable and Unstable Subsystems

Tripathi¹,

Agarwal²

2021

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We study dynamics of a bimodal planar linear switched system with both stable and unstable subsystems. For given flee time from the unstable subsystem, the goal is to find corresponding dwell time in the stable subsystem so that the switched system is stable. The dwell-flee relations obtained are in terms of certain smooth functions of the eigenvalues and (generalized) eigenvectors of the subsystem matrices. The results are then extended to a multimodal planar linear switched system in which the switching is governed by a star graph. In this situation, for given flee time, the computation of dwell-flee relations reduces to a minimax optimization problem.

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