Results 1 to 10 of about 35,286 (235)
Stability of Generalized Proportional Caputo Fractional Differential Equations by Lyapunov Functions [PDF]
Fractal and Fractional, 2022 In this paper, nonlinear nonautonomous equations with the generalized proportional Caputo fractional derivative (GPFD) are considered. Some stability properties are studied by the help of the Lyapunov functions and their GPFDs.
Ravi Agarwal +2 more
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PHSS Iterative Method for Solving Generalized Lyapunov Equations [PDF]
Mathematics, 2019 Based on previous research results, we propose a new preprocessing HSS iteration method (PHSS) for the generalized Lyapunov equation. At the same time, the corresponding inexact PHSS algorithm (IPHSS) is given from the angle of application.
Shi-Yu Li, Hai-Long Shen, Xin-Hui Shao
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Existence and Lyapunov Stability of Periodic Solutions for Generalized Higher-Order Neutral Differential Equations [PDF]
Boundary Value Problems, 2011 Existence and Lyapunov stability of periodic solutions for a generalized higher-order neutral differential equation are established.
Jingli Ren, Wing-Sum Cheung, Zhibo Cheng
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Quadratic Lyapunov Functions for Stability of the Generalized Proportional Fractional Differential Equations with Applications to Neural Networks [PDF]
Axioms, 2021 A fractional model of the Hopfield neural network is considered in the case of the application of the generalized proportional Caputo fractional derivative. The stability analysis of this model is used to show the reliability of the processed information.
Ricardo Almeida +3 more
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Solving Projected generalized Lyapunov Equations using SLICOT
2006 IEEE Conference on Computer-Aided Control Systems Design, 2006 We discuss the numerical solution of projected generalized Lyapunov equations. Such equations arise in many control problems for linear time-invariant descriptor systems including stability analysis, balancing and model order reduction. We present solvers for projected generalized Lyapunov equations based on matrix equations subroutines that are ...
Tatjana Stykel
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Lyapunov Stability of the Generalized Stochastic Pantograph Equation [PDF]
Journal of Mathematics, 2018 The purpose of the paper is to study stability properties of the generalized stochastic pantograph equation, the main feature of which is the presence of unbounded delay functions. This makes the stability analysis rather different from the classical one.
R. I. Kadiev, Arcady Ponosov
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Residual-based iterations for the generalized Lyapunov equation [PDF]
BIT Numerical Mathematics, 2019 This paper treats iterative solution methods to the generalized Lyapunov equation. Specifically it expands the existing theoretical justification for the alternating linear scheme (ALS) from the stable Lyapunov equation to the stable generalized Lyapunov equation.
Tobias Breiten, Emil Ringh
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Generalized Lyapunov functions and functional equations [PDF]
Annali di Matematica Pura ed Applicata, 1965 Some results of Minty and Browder on the existence of solutions of functional equations are generalized by replacing the notion of monotony by one involving a Lyapunov function. In the last section, analogous arguments are used to obtain an existence theorem for an initial value problem belonging to an ordinary differential equation on Hilbert space.
Philip Hartman
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Exact detectability: Application to generalized Lyapunov and Riccati equations
Systems & Control Letters, 2021 This paper is devoted to the application of the recently developed results about exact detectability of a large class of time-varying hybrid stochastic systems (Drăgan et al., 2020). More specifically, we will show from one side the connection between this new detectability notion and the derivation of a criterion for exponential stability in mean ...
Vasile Drǎgan +3 more
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PHSS Iterative Method for Solving Generalized Lyapunov Equations
Mathematics, 2018 Based on previous research results, we propose a new preprocessing HSS iteration method (PHSS) for the generalized Lyapunov equation. At the same time, the corresponding inexact PHSS algorithm (IPHSS) is given from the angle of application. All the new methods presented in this paper have given the corresponding convergence proof.
Shi-Yu Li, Hai-Long Shen, Xin-Hui Shao
openalex +4 more sources