Quadratic Lyapunov functions for systems with state-dependent switching |
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Authors: | Wynita M Griggs Christopher K King Robert N Shorten Oliver Mason |
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Institution: | a Hamilton Institute, National University of Ireland, Maynooth, Co., Kildare, Ireland b Department of Mathematics, Northeastern University, Boston, MA 02115, USA c Institut für Automatisierung und Systemtechnik, Technische Universität Ilmenau, D-98684 Ilmenau, Germany |
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Abstract: | In this paper, we consider the existence of quadratic Lyapunov functions for certain types of switched linear systems. Given a partition of the state-space, a set of matrices (linear dynamics), and a matrix-valued function A(x) constructed by associating these matrices with regions of the state-space in a manner governed by the partition, we ask whether there exists a positive definite symmetric matrix P such that A(x)TP+PA(x) is negative definite for all x(t). For planar systems, necessary and sufficient conditions are given. Extensions for higher order systems are also presented. |
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Keywords: | 15A18 52A10 93D05 |
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