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Russia Izhevsk
Year
2015
Volume
25
Issue
1
Pages
51-59
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Section Mathematics
Title Lyapunov functions and comparison theorems for control systems with impulsive actions
Author(-s) Larina Ya.Yu.a
Affiliations Udmurt State Universitya
Abstract We extend the results of E.L. Tonkov and E.A. Panasenko to differential equations and control systems with impulsive actions. In terms of Lyapunov functions and the Clarke derivative we obtain comparison theorems for systems with impulsive effect. We consider the set $\mathfrak M\doteq\bigl\{(t,x)\in[t_0,+\infty)\times\mathbb{R}^n: x\in M(t)\bigr\},$ defined by continuous function $t\rightarrow M(t)$, where for every $t \in \mathbb R$ the set $M(t)$ is nonempty and compact. We obtain conditions for the positive invariance of this set, the uniform Lyapunov stability and the uniform asymptotic stability. We make a comparison with the researches of other authors who have considered the zero solution stability for similar systems.
Keywords control systems with impulsive actions, Lyapunov function, differential inclusions
UDC 517.935, 517.938
MSC 34A60, 37N35, 49J15, 93B03
DOI 10.20537/vm150106
Received 17 February 2015
Language Russian
Citation Larina Ya.Yu. Lyapunov functions and comparison theorems for control systems with impulsive actions, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2015, vol. 25, issue 1, pp. 51-59.
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