Geodesic
State-feedback control principles for inverted pendulum with hysteresis in suspension
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 9 (2016) no. 4, pp. 498-509.

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In this paper we consider the mathematical model of the inverted pendulum with the hysteretic nonlinearity (in the form of a backlash) under state feedback control. The analytic results for the stability criteria as well as for the solution of the linearized equation are observed and analyzed. The theorems that determine the stabilization of the considered system are formulated and discussed. The question on the optimal control of the system under consideration is also discussed and the corresponding theorem is considered.
Keywords: hysteretic nonlinearity, backlash, feedback principles, optimal control. 
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Mikhail E. Semenov; Zainib Hatif Abbas; Igor N. Ishchuk; Olesya I. Kanishcheva; Peter A. Meleshenko. State-feedback control principles for inverted pendulum with hysteresis in suspension. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 9 (2016) no. 4, pp. 498-509. http://geodesic.mathdoc.fr/item/JSFU_2016_9_4_a13/

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