Abstract
The problem of stabilizing a mathematical hybrid system with switchings between the operating modes is solved. Each of these modes is associated with nonlinear differential equations that have control parameters. The switching instances (conditions) are control components. A stabilizer must be designed in positional form that allows the trajectory of the entire nonlinear system to reach the target set in the phase space for a (prescribed) finite time. To solve the problem, k]an apparatus of continuous piecewise-linear Lyapunov functions is used along with the corresponding piecewise-linear control functions. A theorem concerning the sufficient conditions for the stabilizability of a hybrid system in the considered class of controls is proved. An algorithm for constructing the Lyapunov functions and the stabilizer is given.
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Funding
This work was supported by the Russian Foundation for Basic Research, project nos. 19–01–00613 and 16–29–04191ofi_m.
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Russian Text © The Author(s), 2019, published in Vestnik Moskovskogo Universiteta, Seriya 15: Vychislitel’naya Matematika i Kibernetika, 2019, No. 4, pp. 22–32.
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Atanesyan, A.A., Tochilin, P.A. Problem of Stabilizing a Switching System Using a Piecewise-Linear Control System. MoscowUniv.Comput.Math.Cybern. 43, 166–176 (2019). https://doi.org/10.3103/S0278641919040046
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DOI: https://doi.org/10.3103/S0278641919040046