Abstract
This entry provides a short introduction to modeling of hybrid dynamical systems and then focuses on stability theory for these systems. It provides definitions of asymptotic stability, basin of attraction, and uniform asymptotic stability for a compact set. It points out mild assumptions under which different characterizations of asymptotic stability are equivalent, as well as when an asymptotically stable compact set exists. It also summarizes necessary and sufficient conditions for asymptotic stability in terms of Lyapunov functions.
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Bibliography
Bainov DD, Simeonov PS (1989) Systems with impulse effect: stability, theory, and applications. Ellis Horwood Limited, Chichester
Branicky MS (1998) Multiple Lyapunov functions and other analysis tools for switched and hybrid systems. IEEE Trans Autom Control 43:1679–1684
DeCarlo RA, Branicky MS, Pettersson S, Lennartson B (2000) Perspectives and results on the stability and stabilizability of hybrid systems. Proc IEEE 88(7): 1069–1082
Goebel R, Sanfelice RG, Teel AR (2009) Hybrid dynamical systems. IEEE Control Syst Mag 29(2):28–93
Goebel R, Sanfelice RG, Teel AR (2012) Hybrid dynamical systems. Princeton University Press, Princeton
Haddad W, Chellaboina V, Nersesov SG (2006) Impulsive and hybrid dynamical systems. Princeton University Press, Princeton
Hespanha JP (2004) Uniform stability of switched linear systems: extensions of LaSalle’s invariance principle. IEEE Trans Autom Control 49(4):470–482
Lakshmikantham V, Bainov DD, Simeonov PS (1989) Theory of impulsive differential equations. World Scientific, Singapore/Teaneck
Liberzon D (2003) Switching in systems and control. Birkhauser, Boston
Liberzon D, Morse AS (1999) Basic problems in stability and design of switched systems. IEEE Control Syst Mag 19(5):59–70
Lygeros J, Johansson KH, Simić SN, Zhang J, Sastry SS (2003) Dynamical properties of hybrid automata. IEEE Trans Autom Control 48(1):2–17
Matveev A, Savkin AV (2000) Qualitative theory of hybrid dynamical systems. Birkhauser, Boston
Michel AN, Hou L, Liu D (2008) Stability of dynamical systems: continuous, discontinuous, and discrete systems. Birkhauser, Boston
van der Schaft A, Schumacher H (2000) An introduction to hybrid dynamical systems. Springer, London/New York
Yang T (2001) Impulsive control theory. Springer, Berlin/ New York
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Teel, A.R. (2021). Stability Theory for Hybrid Dynamical Systems. In: Baillieul, J., Samad, T. (eds) Encyclopedia of Systems and Control. Springer, Cham. https://doi.org/10.1007/978-3-030-44184-5_99
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DOI: https://doi.org/10.1007/978-3-030-44184-5_99
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