A pendulum on a moving foundation is modeled as a Takagi–Sugeno impulsive fuzzy system. This makes it possible to analyze the motion of a wheel over a rough surface. The sufficient conditions for the asymptotic stability of the upper position of the pendulum are established
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A. V. Beznos, A. A. Grishin, A. V. Lenskii, et al., “A pendulum controlled by a flywheel,” Dokl. Math., 69, No. 2, 302–307 (2003).
A. A. Grishin, A. V. Lenskii, D. E. Okhotsimsky, et al., “A control synthesis for an unstable object. an inverted pendulum,” J. Comp. Syst. Sci. Int., 41, No. 5, 685–694 (2002).
V. S. Denisenko, “Stability of Takagi–Sugeno fuzzy impulsive systems: Method of linear matrix inequalities,” Dop. NAN Ukrainy, No. 11, 66–73 (2008).
V. S. Denisenko, A. A. Martynyuk, and V. I. Slyn’ko, “On Lyapunov stability of impulsive Takagi–Sugeno fuzzy systems,” Nonlin. Oscill., 11, No. 4, 505–520 (2008).
V. S. Denisenko, A. A. Martynyuk, and V. I. Slyn’ko, “On the mappings preserving the Lyapunov stability of Takagi–Sugeno fuzzy systems,” Ukr. Math. J., 61, No. 5, 764–777 (2009).
Yu. G. Martynenko and A. M. Formalskij, “The theory of the control of a monocycle,” J. Appl. Math. Mech., 69, No. 4, 516–528 (2005).
M. O. Perestyuk and O. S. Chernikova, “Some modern aspects of the theory of impulsive differential equations,” Ukr. Math. J., 60, No. 1, 91–107 (2008).
A. M. Samoilenko and N. A. Perestyuk, Impulsive Differential Equations, World Scientific, Singapore (1995).
V. I. Slyn’ko, Stability of the Motion of Mechanical Systems: Hybrid Models [in Ukrainian], Author’s Abstract of DSci Thesis, Kyiv (2009).
A. M. Formal’skii, “An inverted pendulum on a fixed and a moving base,” J. Appl. Math. Mech., 70, No. 1, 56–64 (2006).
F. A. Aliev and V. B. Larin, “Stabilization problems for a system with output feedback (review),” Int. Appl. Mech., 47, No. 3, 225–267 (2011).
E. Ya. Antonyuk and A. T. Zabuga, “Modeling the maneuvering of a vehicle,” Int. Appl. Mech., 48, No. 4, 447–457 (2012).
Chen-Sheng Ting, “Stability analysis and design of Takagi–Sugeno fuzzy systems,” Inform. Sci., No. 176, 2817–2845 (2006).
V. S. Denisenko, A. A. Martynyuk, and V. I. Slyn’ko, “Stability analysis of impulsive Takagi–Sugeno systems,” Int. J. Innov. Comp. Inform. Contr., 5, No. 10(A), 3141–3155 (2009).
V. S. Denisenko and V. I. Slyn’ko, “Impulsive stabilization of mechanical systems in Takagi–Sugeno models,” Int. Appl. Mech., 45, No. 10, 1127–1140 (2009).
A. I. Dvirnyi and V. I. Slyn’ko, “Stability of impulsive nonholonomic mechanical systems,” Int. Appl. Mech., 44, No. 3, 353–360 (2008).
B. N. Kiforenko, “Problems of the mathematical description of rocket engines as plants,” Int. Appl. Mech., 48, No. 5, 608–612 (2012).
L. G. Lobas and V. Yu. Ichanskii, “Limit cycles of a double pendulum with nonlinear springs,” Int. Appl. Mech., 46, No. 7, 827–834 (2010).
P. S. Simeonov and D. D. Bainov, Impulsive Differential Equations: Periodic Solutions and Applications, Longman, London (1993).
T. Takagi and M. Sugeno, “Fuzzy identification of systems and its applications to modeling and control,” IEEE Trans., Syst. Man. Cybern., No. 15, 116–132 (1985).
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Translated from Prikladnaya Mekhanika, Vol. 49, No. 5, pp. 84–95, September–October 2013.
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Denisenko, V.S., Slyn’ko, V.I. Fuzzy Impulsive Stabilization of the Upper Equilibrium Position of a Pendulum on a Moving Foundation. Int Appl Mech 49, 576–587 (2013). https://doi.org/10.1007/s10778-013-0591-9
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DOI: https://doi.org/10.1007/s10778-013-0591-9