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Quadratic stability and stabilization of bimodal piecewise linear systems |
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| Authors: | Yavuz Eren Jinglai Shen Kanat Camlibel |
| Affiliation: | 1. Department of Control and Automation Engineering, Yildiz Technical University, Esenler 34220, Istanbul, Turkey;2. Department of Mathematics and Statistics, University of Maryland Baltimore Country, MD 21250, Baltimore, USA;3. Department of Mathematics, University of Groningen, P.O. Box 800, 9700 AV Groningen, The Netherlands;4. Department of Electronics and Communication Engineering, Dogus University, Acibadem 34722, Istanbul, Turkey |
| Abstract: | This paper deals with quadratic stability and feedback stabilization problems for continuous bimodal piecewise linear systems. First, we provide necessary and sufficient conditions in terms of linear matrix inequalities for quadratic stability and stabilization of this class of systems. Later, these conditions are investigated from a geometric control point of view and a set of sufficient conditions (in terms of the zero dynamics of one of the two linear subsystems) for feedback stabilization are obtained. |
| Keywords: | Piecewise linear systems Bimodal systems Common quadratic Lyapunov function Quadratic stability Feedback stabilization |
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