Geodesic
On the stability of the equilibrium positions of nonlinear mechanical hybrid system
Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, no. 3 (2015), pp. 116-125

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Stability of trivial equilibrium position of nonlinear mechanical system with switched potential and dissipative forces is studied. The switched system consists of n subsystems described by Rayleigh equations and some switching law determining at each time instant which subsystem is active. It is assumed that potential and dissipative forces are nonlinear and homogeneous. Asymptotic stability of equilibrium position of subsystem is demonstrated. By the use of Lyapunov multiple function and dwell-time approach, the conditions on switching law are obtained. The fulfilment of these conditions provides asymptotic stability of the equilibrium position of switched system. Also the case of known order of switching between the subsystems is considered. An example is presented to demonstrate effectiveness of the proposed approaches. Furthermore it was shown that the equilibrium position may be unstable if switched law is chosen that doesn’t satisfy derived conditions. Refs 11. Figs 2.
Keywords: switched systems, mechanical systems, asymptotic stability, Lyapunov functions, multiple Lyapunov function. 
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     author = {P. A. Lakrisenko},
     title = {On the stability of the equilibrium positions of nonlinear mechanical hybrid system},
     journal = {Vestnik Sankt-Peterburgskogo universiteta. Prikladna\^a matematika, informatika, processy upravleni\^a},
     pages = {116--125},
     publisher = {mathdoc},
     number = {3},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSPUI_2015_3_a9/}
}
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P. A. Lakrisenko. On the stability of the equilibrium positions of nonlinear mechanical hybrid system. Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, no. 3 (2015), pp. 116-125. http://geodesic.mathdoc.fr/item/VSPUI_2015_3_a9/