Archive of Issues
Russia Izhevsk
Section  Mathematics 
Title  Lyapunov functions and comparison theorems for control systems with impulsive actions 
Author(s)  Larina Ya.Yu.^{a} 
Affiliations  Udmurt State University^{a} 
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. 5159. 
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