Results 1 to 10 of about 4,749,057 (127)

On $\Psi$-stability of nonlinear Lyapunov matrix differential equations [PDF]

Electronic Journal of Qualitative Theory of Differential Equations, 2009
We prove necessary and sufficient conditions for $\Psi -$ (uniform) stability of the trivial solution of a nonlinear Lyapunov matrix differential equation.
Aurel Diamandescu
doaj   +5 more sources

On the Ψ − Conditional Exponential Asymptotic Stability of a Nonlinear Lyapunov Matrix Differential Equation with Integral Term as Right Side

Annals of the West University of Timisoara: Mathematics and Computer Science, 2022
The aim of this paper is to give sufficient conditions for Ψ − conditional exponential asymptotic stability of the Ψ − bounded solutions of a nonlinear Lyapunov matrix differential equation with integral term as right side.
Diamandescu Aurel
doaj   +3 more sources

On ψ Bounded Solutions for a Nonlinear Lyapunov Matrix Differential Equation on 𝕉 [PDF]

Annals of the West University of Timisoara: Mathematics and Computer Science, 2018
Using Banach and Schauder - Tychono fixed point theorems, existence results for a nonlinear Lyapunov matrix differential equation on 𝕉 are given. The obtained results generalize and extend the results from [5] and [18].
Diamandescu Aurel
doaj   +2 more sources

The eigenvalue product bounds of the Lyapunov matrix differential equation and the stability of a class of time-varying nonlinear system [PDF]

Journal of Inequalities and Applications, 2019
The Lyapunov matrix differential equation plays an important role in many scientific and engineering fields. In this paper, we first give a class relation between the eigenvalue of functional matrix derivative and the derivative of functional matrix ...
Jianzhou Liu, Juan Zhang, Hao Huang
doaj   +3 more sources

On the Ψ − Conditional Asymptotic Stability of a Nonlinear Lyapunov Matrix Differential Equation with Integral Term as Right Side

Annals of the West University of Timisoara: Mathematics and Computer Science
The aim of this paper is to give sufficient conditions for Ψ − conditional asymptotic stability of the Ψ − bounded solutions of a nonlinear Lyapunov matrix differential equation with integral term as right side.
Diamandescu Aurel
doaj   +2 more sources

Stability analysis of nonlinear Lyapunov systems associated withan nth order system of matrix differential equations [PDF]

International Journal of Stochastic Analysis, 2000
This paper introduces the notion of Lipschitz stability for nonlinear nth order matrix Lyapunov differential systems and gives sufficient conditions for Lipschitz stability. We develop variation of parameters formula for the solution of the nonhomogeneous nonlinear nth order matrix Lyapunov differential system.
Murty, K. N., Shaw, Michael D.
openaire   +4 more sources

Function approximation technique (FAT)-based nonlinear control strategies for smart thin plates with cubic nonlinearities [PDF]

FME Transactions, 2022
The current work introduces three nonlinear control solutions for the regulation of a vibrating nonlinear plate considering model uncertainty. These solutions are feedback linearization control (FBL), virtual velocity error-based control (VVEC), and ...
Al-Shuka Hayder F.N., Abbas Ehab N.
doaj   +1 more source

Physics-Informed Neural Networks and Functional Interpolation for Solving the Matrix Differential Riccati Equation

Mathematics, 2023
In this manuscript, we explore how the solution of the matrix differential Riccati equation (MDRE) can be computed with the Extreme Theory of Functional Connections (X-TFC). X-TFC is a physics-informed neural network that uses functional interpolation to
Kristofer Drozd, Roberto Furfaro, Enrico Schiassi, Andrea D’Ambrosio   +3 more
doaj   +1 more source

Classification of Chaotic Signals of the Recurrence Matrix Using a Convolutional Neural Network and Verification through the Lyapunov Exponent

Applied Sciences, 2020
This study classified chaotic time series data, including smooth and nonsmooth problems in a dynamic system, using a convolutional neural network (CNN) and verified it through the Lyapunov exponent. For this, the classical nonlinear differential equation
Jaehyeon Nam, Jaeyoung Kang
doaj   +1 more source

Approximate Methods for Solving Linear and Nonlinear Hypersingular Integral Equations

Axioms, 2020
We propose an iterative projection method for solving linear and nonlinear hypersingular integral equations with non-Riemann integrable functions on the right-hand sides.
Ilya Boykov, Vladimir Roudnev, Alla Boykova   +2 more
doaj   +1 more source