Instability in the simplest class of continuous switched linear systems with stable components
| Authors: | Ponce Enrique, University of Sevilla, Spain
Carmona Victoriano, University of Sevilla, Spain
Freire Emilio, University of Sevilla, Spain
Torres Francisco, University of Sevilla, Spain |
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| Topic: | 2.3 Non-Linear Control Systems |
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| Session: | Nonlinear Stability II |
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| Keywords: | Piecewise linear systems, switched systems, stability |
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Abstract
For discontinuous switched linear systems, even when they arebuilt by composing stable systems, examples of unstable systemsare known. Here, three-dimensional homogeneous continuouspiecewise linear systems composed by two linear systems sharing aboundary plane are considered. If the two linearization matricesare non-singular, then the only equilibrium point is at theorigin, which is in the separation plane of the linear regions.For the important case where both matrices have complexeigenvalues and their whole spectra are in the open-left half ofthe complex plane, the possible counter-intuitive instability ofthe origin is analytically proved. Thus, in this paper, examplesof unstable continuous switched linear system with just two stablecomponents are shown.
