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Stability and Stabilization of Two‐Dimensional LTI Switched Systems with Potentially Unstable Focus
Author(s) -
Zhu Liying
Publication year - 2015
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1002/asjc.938
Subject(s) - control theory (sociology) , exponential stability , lti system theory , focus (optics) , stability (learning theory) , instability , linear system , mathematics , positive definite matrix , invariant (physics) , state (computer science) , computer science , mathematical analysis , control (management) , physics , eigenvalues and eigenvectors , nonlinear system , algorithm , optics , quantum mechanics , artificial intelligence , machine learning , mechanics , mathematical physics
This paper investigates stability and stabilization of two‐dimensional switched linear time‐invariant (LTI) systems with potentially unstable focus. For the case that the origin is a single common focus of all subsystems, we first give continuous positive definite functions related only to the elements of subsystems' state matrices. Then, based on the continuous positive definite functions obtained, this paper proposes several sufficient conditions of stability/asymptotic stability/instability of the kind of switched LTI systems. By means of the stability results proposed, global asymptotic stabilizing controls (GASC), global asymptotic stabilizing switching paths (GASSP) and corresponding algorithms are designed for two‐dimensional switched LTI systems with focus. Finally, two illustrative examples and numerical simulations demonstrate the effectiveness of the new stability and stabilization results obtained in this paper.