Alexander N. Sesekin     (Krasovskii Institute of Mathematics and Mechanics, Ural Branch of Russian Academy of Sciences, Ekaterinburg, Russian Federation)
Natalya I. Zhelonkina     (Krasovskii Institute of Mathematics and Mechanics, Ural Branch of Russian Academy of Sciences, Ekaterinburg, Russian Federation)


The paper is devoted to the formalization of a concept of impulse-sliding regimes generated by positional impulse controls for systems with delay. We define the notion of impulse-sliding trajectory as a limit of a sequence of Euler polygonal lines generated by a discrete approximation of the impulse position control. The equations describing the trajectory of impulse-sliding regime are received.


Impulse position control, Systems with delay, Impulse-sliding regime, The Euler polygons

Full Text:



Zavalishchin S.T., Sesekin A.N. Impulse-sliding regimes of nonlinear dynamic systems // Differ. Equations. 1983. Vol. 19, no. 5, P. 562–571.

Finogenko I.A., Ponomarev D.V. About differential inclusions with positional explosive and impulsive controls // Trudy Inst. Mat. i Mekh. UrO RAN, 19, no. 1, 2013, 284–299. [in Russian]

Sesekin A.N., Nepp A.N. Impulse position control algorithms for nonlinear systems // AIP Conference Proceeding. 2015. Vol. 1690, P. 040002 1–6. DOI:10.1063/1.4936709

Andreeva I.Yu., Sesekin A.N. Degenerate linear–quadratic optimization with time delay // Autom. Remote Control. 1997. Vol. 58, no. 7. P. 1101–1109.

Fetisova Yu.V., Sesekin A.N. Discontinuous solutions of differential equations with time delay // WSEAS transactions on systems. 2005. Vol. 4, no. 5. P. 487–492.

Zavalishchine S.T, Sesekin A.N. Dynamic impulse systems: theory and applications. Kluwer Academic Publishers. Dolrbrecht, 1997. 256 p.

Sesekin A.N. Dynamic systems with nonlinear impulse structure // Proc. Steklov Inst. Math., 2000. No. Suppl. 2, S158–S172.

Cartan H. Formes differentielles Calcul differentiel. Hermann Paris, 1997.

Lukojanov N.Yu. Functional equations of Hamilton-Jacobi and control tasks with hereditary information. Ural Federal University. Ekaterinburg, 2011. P. 243. [in Russian]

Bellman R., Cooke K. Differential-difference equations. Academik Press. New Yourk, London, 1963.

Filippov A.F. The existence of solutions of generalized differential equations // Mathematical Notes, 1971. Vol. 10, no. 3. P. 307–313.


Article Metrics

Metrics Loading ...


  • There are currently no refbacks.