Componentwise ultimate bound and invariant set computation for switched linear systems |
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Authors: | H Haimovich [Author Vitae] MM Seron [Author Vitae] |
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Affiliation: | a CONICET and Laboratorio de Sistemas Dinámicos y Procesamiento de Información, Departamento de Control, Facultad de Cs. Exactas, Ingeniería y Agrimensura, Universidad Nacional de Rosario, Riobamba 245bis, 2000 Rosario, Argentinab ARC Centre for Complex Dynamic Systems & Control, The University of Newcastle, Callaghan, NSW 2308, Australia |
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Abstract: | We present a novel ultimate bound and invariant set computation method for continuous-time switched linear systems with disturbances and arbitrary switching. The proposed method relies on the existence of a transformation that takes all matrices of the switched linear system into a convenient form satisfying certain properties. The method provides ultimate bounds and invariant sets in the form of polyhedral and/or mixed ellipsoidal/polyhedral sets, is completely systematic once the aforementioned transformation is obtained, and provides a new sufficient condition for practical stability. We show that the transformation required by our method can easily be found in the well-known case where the subsystem matrices generate a solvable Lie algebra, and we provide an algorithm to seek such transformation in the general case. An example comparing the bounds obtained by the proposed method with those obtained from a common quadratic Lyapunov function computed via linear matrix inequalities shows a clear advantage of the proposed method in some cases. |
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Keywords: | Ultimate bounds Invariant sets Switched systems Componentwise methods Solvable Lie algebras |
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