Abstract
The stationary state of a continuous hybrid system is analyzed for stability using the method of Lyapunov functions. Sufficient conditions of stability and instability are established. These conditions are constructive and can easily be calculated.
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S. V. Emel’yanov (ed.), Theory of Variable-Structure Systems [in Russian], Nauka, Moscow (1972).
O. Bychkov, “Applying the second Lyapunov method to analyze hybrid systems for stability,” Visn. Kyiv. Univ., Ser. Fiz. Mat. Nauk, No. 4, 125–133 (2005).
N. P. Buslenko, Simulation of Complex Systems [in Russian], Nauka, Moscow (1978).
E. Yu. Pariiskaya, “A hybrid approach to simulation and qualitative analysis of dynamic systems. Algorithms of linear approximation of a nonlinear hybrid automaton,” in: Proc. 2nd Intern. Sci.-Techn. Conf. on Differential Equations and Applications [in Russian], St. Petersburg (1998), pp. 174–177.
V. M. Glushkov, V. V. Gusev, T. P. Mar’yanovich, and M. A. Sakhnyuk, Software for Modeling Continuous-Discrete Systems [in Russian], Naukova Dumka, Kyiv (1975).
Y. Kesten and A. Pnueli, “Timed and hybrid statecharts and their textual representation,” Lect. Notes Comp. Sci., 571, 591–620 (1992).
D. Liberzon and A. S. Morse, “Basic problems in stability and design of switched systems,” IEEE Contr. Syst. Mag., 19, No. 5, 59–70 (1999).
S. Pettersson and B. Lennartson, “Stability and robustness for hybrid systems,” in: Proc. 35th CDC, Kobe (Japan) (1996), pp. 1202–1207.
H. Ye, A. N. Michel, and L. Hou, “Stability theory for hybrid dynamical systems,” IEEE Trans. Autom. Control, 43, No. 4, 461–474 (1998).
P. Peleties and R. DeCarlo, “Asymptotic stability of m-switched systems using Lyapunov-like functions,” in: Proc. Amer. Control Conf., Boston (MA) (1991), pp. 1679–1684.
M. Branicky, “Stability of switched and hybrid systems,” in: Proc. 33rd Conf. Decision and Control, Lake Buena Vista (FL) (1994), pp. 3498–3503.
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Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 123–128, March–April 2007.
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Bychkov, A.S., Merkur’ev, M.G. Stability of continuous hybrid systems. Cybern Syst Anal 43, 261–265 (2007). https://doi.org/10.1007/s10559-007-0045-7
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DOI: https://doi.org/10.1007/s10559-007-0045-7