Abstract
We obtain conditions for the technical stability, with respect to a given measure, of autonomous dynamical systems with a discontinuous control for all possible initial conditions ranging over a given region of admissible initial perturbations of the processes under consideration. The formulated criteria depend on properties of roots of the secular equation of a given quadratic form corresponding to the control system under investigation.
Similar content being viewed by others
References
L. T. Ashchepkov, Optimal Control of Discontinuous Systems [in Russian], Nauka, Novosibirsk (1987).
E. A. Barbashyn, Introduction to Stability Theory [in Russian], Nauka, Moscow (1967).
F. G. Garashchenko andN. F. Kirichenko, “A study of problems on practical stability and stabilization of motion, ” Mekh. Tverd. Tela, No. 6, 15–24 (1975).
S. V. Emel'yanov,V. I. Utkin,V. A. Taran, and others, The Theory of Systems with a Changing Structure [in Russian], Nauka, Moscow (1970).
N. F. Kirichenko, Some Problems of Stability and Controllability of Motion [in Russian], Izd. Kiev University, Kiev (1972).
V. M. Kuntsevich andM. M. Lychak, A Synthesis of Automatic Control Systems with Lyapunov Functions [in Russian], Nauka, Moscow (1977).
K. S. Matvi\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{\imath}\)chuk, “On a study of the technical stability of systems with dumping elements, ” Prikl. Mekh., 19, No. 5, 100–106 (1983).
K. S. Matvi\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{\imath}\)chuk, “On the technical stability of automatic control systems with a changing structure, ” Prikl. Mekh., 30, No. 10, 74–78 (1994).
A. F. Fillipov, Differential Equations with Discontinuous Right-Hand Side [in Russian], Nauka, Moscow (1985).
M. A. Lavrentiev andL. A. Lyusternik, Fundamentals of Calculus of Variations [in Russian], Vol. 1, ONTI, Moscow-Leningrad (1935).
J. Szarski, Differential Inequalities, PWN, Warszawa (1967).
Rights and permissions
About this article
Cite this article
Matviichuk, K.S. Technical Stability of an Automatic Control System with a Changing Structure in the Neutral Case. Journal of Mathematical Sciences 107, 3776–3786 (2001). https://doi.org/10.1023/A:1012362418267
Issue Date:
DOI: https://doi.org/10.1023/A:1012362418267