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Multivariate Lipschitz Analysis of the Stability of Neural Networks
Frontiers in Signal Processing, 2022 The stability of neural networks with respect to adversarial perturbations has been extensively studied. One of the main strategies consist of quantifying the Lipschitz regularity of neural networks.
Kavya Gupta +5 more
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Lipschitz Stability in Time for Riemann–Liouville Fractional Differential Equations
Fractal and Fractional, 2021 A system of nonlinear fractional differential equations with the Riemann–Liouville fractional derivative is considered. Lipschitz stability in time for the studied equations is defined and studied.
Snezhana Hristova +2 more
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Lipschitz Stability in Terms of Two Measures for Kurzweil Equations and Applications
Mathematics, 2023 For generalized ordinary differential equations, sufficient criteria are given for the Lipschitz stability in terms of two measures of the trivial solutions.
Yingying Wang, Zhinan Xia
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IET Control Theory & Applications, 2023 In this study, the stability of a sampled‐value control system with time‐ and state‐dependent disturbance and aperiodic sampling is investigated. To expand the application class of the sampled‐value controller, the local stability on a compact set is ...
Kazuki Umemoto +2 more
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Practical Mittag-Leffler stability of quasi-one-sided Lipschitz fractional order systems [PDF]
Archives of Control Sciences, 2023 This paper focuses on the global practical Mittag-Leffler feedback stabilization problem for a class of uncertain fractional-order systems. This class of systems is a larger class of nonlinearities than the Lipschitz ones.
Imed Basdouri, Souad Kasmi, Jean Lerbet
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Electronic Journal of Qualitative Theory of Differential Equations, 2019 We consider a class of retarded functional differential equations with preassigned moments of impulsive effect and we study the Lipschitz stability of solutions of these equations using the theory of generalized ordinary differential equations and ...
Suzete Afonso, Márcia da Silva
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Fractal and Fractional, 2022 This paper investigates set-valued differential equations with fractional-like Hukuhara derivatives. Firstly, a novel comparison principle is given by introducing the upper quasi-monotone increasing functions.
Peiguang Wang, Jiahui Bi
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Axioms, 2018 In this paper, we study Lipschitz stability of Caputo fractional differential equations with non-instantaneous impulses and state dependent delays. The study is based on Lyapunov functions and the Razumikhin technique. Our equations in particular include
Ravi Agarwal +2 more
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Some stability inequalities for hybrid inverse problems
Comptes Rendus. Mathématique, 2022 We study some hybrid inverse problems associated to BVP’s for Schrödinger and Helmholtz type equations. The inverse problems we consider consist in the determination of coefficients from the knowledge of internal energy densities.
Choulli, Mourad
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On eventual stability of impulsive systems of differential equations
International Journal of Mathematics and Mathematical Sciences, 2001 The notions of Lipschitz stability of impulsive systems of differential equations are extended and the notions of eventual stability are introduced. New notions called eventual and eventual Lipschitz stability. We give some criteria and results.
A. A. Soliman
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