On Stability of Linear Systems with Impulsive Action at the Matrix
- 16 Downloads
We discuss properties of stability and asymptotic stability of solutions to linear systems of differential equations with generalized actions in matrices of systems. We obtain sufficient conditions that guarantee the stability and asymptotic stability of solutions to these system. A distinctive feature of systems considered is the fact that the right-hand sides of systems contain the ill-posed operation of multiplication of discontinuous functions by generalized functions.
Keywords and phrasesdifferential equation impulsive action stability asymptotic stability
AMS Subject Classification34K45
Unable to display preview. Download preview PDF.
- 1.D. L. Andrianov, V. O. Arbuzov, S. V. Ivliev, V. P. Maksimov, and P. M. Simonov, “Dynamical models of Economics: Theory, applications, and software,” Vestn. Perm. Univ. Ser. Ekon., 27, No. 4, 8–32 (2015).Google Scholar
- 3.I. A. Kornilov and A. N. Sesekin, “On stability of linear systems with matrix containing generalized functions,” Vestn. UGTU-UPI, 33, No. 3, 386–388 (2004).Google Scholar
- 4.V. P. Maksimov, “Positional parring of impulsive perturbances in a control problem for linear systems with aftereffect,” Vestn. Perm. Univ. Ser. Ekon., 21, No. 2, 6–14 (2014).Google Scholar
- 5.B. M. Miller and V. Ya. Rubinovich, “Discontinuous solutions to optimal control problems and their representation by singular space-time transforms,” Avtomat. Telemekh., No. 12, 56–103 (2013).Google Scholar
- 6.A. M. Samoilenko and N. A. Perestyuk, Differential Equations with Impulsive Actions pin Russian], Vyshcha Shkola, Kiev (1987).Google Scholar
- 7.A. N. Sesekin, “Dynamical systems with nonlinear impulsive structure,” Tr. Inst. Mat. Mekh. Ural Otd. Ross. Akad. Nauk, 6, No. 2, 497–514 (2000).Google Scholar
- 8.A. N. Sesekin and N. I. Zhelonkina, “On the stability of linear systems with generalized action and delay,” Proc. 18th IFAC World Congr., IFAC-PapersOnLine, 13404–13407, Milano, Italy (2011).Google Scholar
- 9.S. T. Zavalishchin and A. N. Sesekin, Dynamic Impulse Systems: Theory and Applications, Kluwer, Dordrecht (1997).Google Scholar