2021/11/15 by Swapnil Tripathi, Nikita Agarwal, Tripathi, Swapnil +1
Mathematics · Physics and Astronomy · #37N35 (Primary) #93C05 #93D20 (Secondary) #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Nonlinear Differential Equations Analysis #Quantum chaos and dynamical systems #math.DS #msc:37N35 #msc:93C05 #msc:93D20
paper · pdf · doi:10.48550/arxiv.2111.07543
openalex publication_date 2021/11/15 · arxiv created 2022/04/07 · arxiv updated 2022/04/08 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28
We study dynamics of a bimodal planar linear switched system with a Hurwitz stable and an unstable subsystem. For given flee time from the unstable subsystem, the goal is to find corresponding dwell time in the Hurwitz stable subsystem so that the switched system is asymptotically 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 extended to a special class of symmetric bilinear systems. The results are also extended to a multimodal planar linear switched system in which the switching is governed by an undirected star graph, where the internal node corresponds to a Hurwitz stable (unstable, respectively) subsystem and all the leaves correspond to unstable (Hurwitz stable, respectively) subsystems. For this multimodal system, dwell-flee relations are obtained as solutions of a minimax optimization problem.