Quadratic Lyapunov Functions for Stability of the Generalized Proportional Fractional Differential Equations with Applications to Neural Networks

R Almeida, RP Agarwal, S Hristova, D O'Regan - Axioms, 2021 - mdpi.com
stability and the Mittag–Leffler stability of the equilibrium. For this, we extend the second
method of Lyapunov in … We emphasize that the regular stability has not been investigated yet. In …

Lyapunov stability for measure differential equations

C D'Apice, R Manzo, B Piccoli… - Mathematical Control and …, 2024 - aimsciences.org
… discuss two concepts related to classical Lyapunov stability in … On the other hand, MDEs
can be used to study classical control … Notice that we use the brackets for the argument of V to …

Lyapunov-equation-based stability analysis for switched linear systems and its application to switched adaptive control

S Yuan, M Lv, S Baldi, L Zhang - IEEE Transactions on …, 2020 - ieeexplore.ieee.org
… results of Theorem 3.1 and of Corollary 3.2: despite using different Lyapunov functions, we
have that the two results are equivalent in terms of achievable dwell time, as discussed in the …

On the asymptotic stability of solutions of stochastic differential delay equations of second order

O Tunç, C Tunç - Journal of Taibah University for Science, 2019 - Taylor & Francis
… as stability analysis, convergence analysis, asymptotic analysis… , for linear and non-linear
delay differential equations (DDEs) of … In this paper, the second functional method of Lyapunov-…

The connections between Lyapunov functions for some optimization algorithms and differential equations

JM Sanz Serna, KC Zygalakis - SIAM Journal on Numerical Analysis, 2021 - SIAM
study the properties of a family of a second-order differential … For f \in Fm,L, we use the LMI
framework from [8] to derive … for a two-parameter family of Nesterov optimization methods (see …

Converse theorems in Lyapunov's second method and applications for fractional order systems

J GALLEGOS… - Turkish Journal of …, 2019 - journals.tubitak.gov.tr
… the existence of Lyapunov functions for stable systems (see [12… results for differential equations;
before trying any function as a … With their application, a linearization equivalence to study

Qualitative analyses of integro-fractional differential equations with Caputo derivatives and retardations via the Lyapunov–Razumikhin method

O Tunç, Ö Atan, C Tunç, JC Yao - Axioms, 2021 - mdpi.com
… The purpose of this paper is to investigate some qualitative … two methods mentioned, the
second Lyapunov method and … plan to investigate the uniformly stability, asymptotic stability, …

Lyapunov functions for fractional-order systems in biology: Methods and applications

A Boukhouima, K Hattaf, EM Lotfi, M Mahrouf… - Chaos, Solitons & …, 2020 - Elsevier
… are very successful and simple to solve differential equations with … method is presented
with proofs. Then, in Section 3, we apply our method to study the asymptotic stability of two

The direct method of Lyapunov for nonlinear dynamical systems with fractional damping

M Hinze, A Schmidt, RI Leine - Nonlinear Dynamics, 2020 - Springer
differential equations with infinite delay and use the associated stability concept and
known theorems regarding Lyapunov … Finally, we study the example of a two degree-of-freedom …

Computation of the Lyapunov matrix for periodic time-delay systems and its application to robust stability analysis

MA Gomez, AV Egorov, S Mondié, AP Zhabko - Systems & Control Letters, 2019 - Elsevier
Lyapunov matrix for periodic time-delay systems that is based on the numerical solution of
a partial differential equations (… is stable and (ii) they are determined by the delay Lyapunov