Larina, Ya. Yu. Lyapunov functions and comparison theorems for control systems with impulsive actions. (Russian. English summary) Zbl 1333.34024 Vestn. Udmurt. Univ., Mat. Mekh. Komp’yut. Nauki 25, No. 1, 51-59 (2015). Summary: We extend the results of E. A. Panasenko and E. L. Tonkov [Proc. Steklov Inst. Math. 268, S204-S221; translation from Tr. Inst. Mat. Mekh. (Ekaterinburg) 15, No. 3, 185–201 (2009; Zbl 1302.93182)] 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 \(\mathfrak M\doteq\bigl\{(t,x)\in[t_0,+\infty)\times\mathbb R^n\colon x\in M(t)\bigr\}\), defined by continuous function \(t \to M(t)\), 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. Cited in 1 Document MSC: 34A37 Ordinary differential equations with impulses 34A60 Ordinary differential inclusions 49J15 Existence theories for optimal control problems involving ordinary differential equations 34D20 Stability of solutions to ordinary differential equations 34H05 Control problems involving ordinary differential equations 34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations Keywords:control systems with impulsive actions; Lyapunov function; differential inclusions Citations:Zbl 1302.93182 PDFBibTeX XMLCite \textit{Ya. Yu. Larina}, Vestn. Udmurt. Univ., Mat. Mekh. Komp'yut. Nauki 25, No. 1, 51--59 (2015; Zbl 1333.34024) Full Text: DOI MNR