References
Barbashin E. A., An Introduction to Stability Theory, [in Russian], Nauka, Moscow (1967).
Emel'yanov S. V. et al., The Theory of Systems with Variable Structure [in Russian], Nauka, Moscow (1970).
Utkin V. I., Sliding Modes in Optimization and Control Problems [in Russian], Nauka, Moscow (1989).
Lozgachev G. I., “On construction of Lyapunov functions for systems with variable structure,” Avtomat. i Telemekh., No. 8, 161–162 (1972).
Zubov V. I., Lectures on Control Theory, [in Russian], Nauka, Moscow (1975).
Ashchepkov L. T., Optimal Control of Discontinuous Systems [in Russian], Nauka, Novosibirsk (1987).
Meshchanov A. S., An Application of Lyapunov Functions in Constructing Discontinuous Controls [in Russian], Nauka, Novosibirsk (1983).
Filippov A. F., Differential Equations with a Discontinuous Right-Hand Side [in Russian], Nauka, Moscow (1985).
Khapaev M. M., “Conditions for controllability of singularly perturbed systems involving singular controls,” Dokl. Akad. Nauk SSSR,320, No. 2, 300–302 (1991).
Kamenkov G. V., “On stability over a finite time interval,” Prikl. Mat. Mekh.,17, No. 5, 529–540 (1953).
Kirichenko N. F., Some Stability and Controllability Problems of Motion [in Russian], Kiev Univ., Kiev (1972).
Garashchenko F. G. andKirichenko N. F., “Study of problems on practical stability and stabilization of motion,” Mekh. Tverd. Tela, No. 6, 15–24 (1975).
Garashchenko F. G., “On some problems of dynamical stability and some of their applications” Vychisl. i Prik. Mat., No. 46, 106–112 (1982).
Korenevskiî, D. G., “Certain criteria for stability of linear stationary systems with delay,” Dop. Akad. Nauk Ukrain. SSR, No. 6, 708–710 (1966).
Kuntsevich V. M. andLychak M. M., Synthesis of Automatic Control Systems by Lyapunov Functions [in Russian], Nauka, Moscow (1977).
Chekhovoî Yu. N., “An application of the Lyapunov function method to some quasilinear problems of stability theory of modulated systems,” in: Lyapunov Functions and Some of Their Applications [in Russian], Nauka, Novosibirsk, 1986, pp. 78–90.
Gromondz V. T., “To a problem of stability over a finite time interval,” in: Problems of Analytical Mechanics, Stability, and Control of a Motion [in Russian], Nauka, Novosibirsk, 1991, pp. 62–68.
Baîramov F. D., “Guaranteeing engineering stability of control systems,” in: Problems of Analytical Mechanics, Stability, and Control of a Motion [in Russian], Nauka, Novosibirsk, 1991, pp. 134–139.
Matviîchuk K. S., “On engineering stability of control processes with concentrated parametters,” Prikl. Mekh.,33, No. 2, 74–79 (1997).
Matviîchuk K. S., “On engineering stability of the motion of two connected platforms carrying moving flywheels,” Izv. Ross. Akad. Nauk SSSR Mekh. Tverd. Tela, No. 6, 3–10 (1993).
Matviîchuk K. S., “On engineering stability of parametrically excited distributed processes,” Prikl. Mat. Mekh.,50, No. 2, 210–218 (1986).
Matrosov V. M., Anapol'skiî L. Yu, andVasil'ev S. N., The Comparison Method in the Mathematical Theory of Systems [in Russian] [in Russian], Nauka, Novosibirsk (1980).
Vasil'ev S. N., “On controllability of nonlinear systems under phase constraints and permanent perturbations,” Izv. Ross. Akad. Nauk SSSR Tekhn. Kibernet., No. 1, 77–82 (1993).
Letov A. M., Mathematical Theory of Control Processes [in Russian], Nauka, Moscow (1981).
Pustovoîtov N. A., “Algorithmization problems of the second Lyapunov method,” in: The Direct Method in Stability Theory and Its Applications [in Russian], Nauka, Novosibirsk, 1981, pp. 124–131.
Sirazetdinov T. K., “The Lyapunov function method for studying some properties of processes with aftereffect,” in: The Direct Method in Stability Theory and Its Applications [in Russian], Nauka, Novosibirsk, 1981, pp. 64–75.
Babkin, B. I., “To S. A. Chaplygin's theorem of differential inequalities,” Mat. Sb.,46, No. 4, 389–398 (1958).
Szarski J, Differential Inequalities, PWN, Warszawa (1967).
Skalmierski B. andTylikowski A., Stabilnose Uklalow Dynamicznych, PWN, Warszawa (1973).
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Kiev. Translated fromSibirskiî Matematicheskiî Zhurnal, Vol. 41, No. 4, pp. 873–885, July–August, 2000.
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Matviichuk, K.S. On conditions for engineering stability of dynamical systems with variable structure. Sib Math J 41, 725–736 (2000). https://doi.org/10.1007/BF02679697
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DOI: https://doi.org/10.1007/BF02679697