Author
A. O. Ignat'ev
Bio: A. O. Ignat'ev is an academic researcher. The author has contributed to research in topics: Exponential stability. The author has an hindex of 1, co-authored 1 publications receiving 14 citations.
Topics: Exponential stability
Papers
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TL;DR: In this article, the sufficient conditions for the asymptotic stability of impulsive systems obtained by Gurgula and Perestyuk are shown to be necessary and sufficient conditions.
Abstract: We prove that the sufficient conditions for the asymptotic stability of impulsive systems obtained by Gurgula and Perestyuk are also necessary conditions.
14 citations
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TL;DR: In this article, the stability of the zero solution of a system of ordinary differential equations subject to impulse action was studied using the method of Lyapunov functions, and tests for asymptotic stability or instability of the system were given.
Abstract: In this paper, we study the stability of the zero solution of a system of ordinary differential equations subject to impulse action. Using the method of Lyapunov functions, we obtain tests for asymptotic stability or instability of the system. Illustrative examples are given.
32 citations
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TL;DR: A brief survey of the main results obtained in recent years in the theory of impulsive differential equations can be found in this paper, where the authors give a brief survey on the main main results.
Abstract: We give a brief survey of the main results obtained in recent years in the theory of impulsive differential equations.
25 citations
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TL;DR: In this paper, the system of difference equations x n + 1 = f n (x n ), f n(x n) = 0, n = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22, 23, 24, 25, 26, 27, 28, 28
19 citations
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TL;DR: Necessary and sufficient conditions for the uniform asymptotic stability of the invariant set of a nonlinear impulsive system are established in this paper, where the invariants are defined in terms of a set of invariants.
Abstract: Necessary and sufficient conditions for the uniform asymptotic stability of the invariant set of a nonlinear impulsive system are established
7 citations
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TL;DR: In this article, the robust stability conditions for matrix polytopes of linear systems with impulsive influence were studied and shown to be equivalent to the feasibility problem for a system of linear matrix inequalities in the class of positive definite matrices.
Abstract: We give sufficient robust stability conditions for matrix polytopes of linear systems with impulsive influence. The methods of our study are based on logarithmic matrix measure theory and linear operator theory in Banach spaces. Our results reduce the robust stability problem to the feasibility problem for a system of linear matrix inequalities in the class of positive definite matrices.
5 citations