Abstract
A method for specifying the differential equations with a discontinuous right-hand side was proposed. It allows one to describe all kinds of the right motions of some classes of controllable discontinuous systems. The method is implicit and relies on the necessary existence conditions for the right solutions of equations in the contingencies obtained from the original system.
Similar content being viewed by others
REFERENCES
Aizerman, M.A. and Pyatnitskii, E.S., Fundamentals of the Theory of Discontinuous Systems. I, II, Avtom. Telemekh., 1974, no. 7, pp. 33-47; no. 8, pp. 39-61.
Filippov, A.F., Differentsial'nye uravneniya s razryvnoi pravoi chast'yu (Differential Equations with Discontinuous Right-hand Side), Moscow: Nauka, 1985.
Matrosov, V.M., On Differential Equations and Inequalities with Discontinuous Right-hand Sides. I, II, Diff. Uravn., 1967, vol. 3, no. 3, pp. 395-409; no. 5, pp. 839-848.
Tolstonogov, A.A., Differentsial'nye vklyucheniya v banakhovom prostranstve (Differential Inclusions in the Banach Space), Novosibirsk: Nauka, 1986.
Utkin, V. I., Skol'zyashchie rezhimy v zadachakh optimizatsii i upravleniya, Moscow: Nauka, 1981. Translated into English under the title Sliding Modes in Control Optimization, Heidelberg: Springer, 1992.
Filippov, A.F., On some Issues of the Optimal Control Theory, Vestn. MGU, 1959, no. 2, pp. 25-32.
Pyatnitskii, E.S., Decomposition-based Design of the Hierarchical Control Systems of Mechanical and Electromechanical Plants I, II, Avtom. Telemekh., 1989, no. 1, pp. 87-98; no. 2, pp. 57-70.
Matyukhin, V.I., Stability of the Manifolds of the Manipulator Controllable Motions, Avtom. Telemekh., 1998, no. 4, pp. 47-56.
Matyukhin, V.I., Motional Stability of the Manipulation Robots in the Decomposition State, Avtom. Telemekh., 1989, no. 3, pp. 33-44.
Matrosov, V.M. and Finogenko, I.A., On Solvability of the Motion Equation of Mechanical Systems with Gliding Friction, Prikl. Mat. Mekh., 1994, vol. 58, no. 6, pp. 3-13.
Lur'e, A.I., Analiticheskaya mekhanika (Analytical Mechanics), Moscow: Fizmatgiz, 1961.
Appel', P., Teoreticheskaya mekhanika (Theoretical Mechanics), Moscow: Fizmatgiz, 1960, vol. 2.
Kantorovich, L.V. and Akilov, G.P., Funktsional'nyi analiz (Functional Analysis), Moscow: Nauka, 1977.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Finogenko, I.A. On the Right Solutions of a Class of Discontinuous Systems. I. Automation and Remote Control 62, 1534–1542 (2001). https://doi.org/10.1023/A:1011660129113
Issue Date:
DOI: https://doi.org/10.1023/A:1011660129113