Introduction to Hybrid Dynamical Systems
Introduction to Hybrid Dynamical Systems
Stability of Planar Switched Systems: The Linear Single Input Case
SIAM Journal on Control and Optimization
Towards a stability theory of general hybrid dynamical systems
Automatica (Journal of IFAC)
Automatica (Journal of IFAC)
Stability analysis for 2-dimensional switched linear systems
ACC'09 Proceedings of the 2009 conference on American Control Conference
A graph approach for stability of piecewise linear systems
CCDC'09 Proceedings of the 21st annual international conference on Chinese Control and Decision Conference
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This paper provides several stability tests for piecewise linear systems and proposes a method of stabilization for bimodal systems. In particular, we derive an explicit and exact stability test for planar systems, which is given in terms of coefficients of transfer functions of subsystems. Restricting attention to the bimodal and planar case, we show simple stability tests. In addition, we drive a necessary stability condition and a sufficient stability condition for higher-order and bimodal systems. They are given in terms of the eigenvalue loci and the observability of subsystems. All the stability tests provided in this paper are computationally tractable, and our results are applied to the stabilizability problem. We confirm the exactness and effectiveness of our approach by illustrative examples.