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On Vector Lyapunov Functions [PDF]

Proceedings of the American Mathematical Society, 1971
It has been proved that the use of a vector Lyapunov function is more advantageous in certain situations rather than a scalar function. Moreover, each function needs to satisfy less rigid requirements. In this paper a new situation has been considered where vector Lyapunov functions play a further useful role. For this purpose, a new type of stability,
openaire   +1 more source

Error analysis of QR algorithms for computing Lyapunov exponents [PDF]

, 2001
Lyapunov exponents give valuable information about long term dynamics. The discrete and continuous QR algorithms are widely used numerical techniques for computing approximate Lyapunov exponents, although they are not yet supported by a general error ...
McDonald, E.J., Higham, D.J.
core   +4 more sources

Physics-informed transient stability assessment of microgrids

iEnergy, 2023
With the integration of a voltage source converter (VSC), having variable internal voltages and source impedance, in a microgrid with high resistance to reactance ratio of short lines, angle-based transient stability techniques may find limitations ...
Priyanka Mishra, Peng Zhang
doaj   +1 more source

Lyapunov Functionals in Integral Equations

Axioms, 2023
Lyapunov functions/functionals have found their footing in Volterra integro-differential equations. This is not the case for integral equations, and it is therefore further explored in this paper. In this manuscript, we utilize Lyapunov functionals combined with Laplace transform to qualitatively analyze the solutions of the integral equation In ...
Youssef N. Raffoul, Joseph Raffoul
openaire   +3 more sources

Learning lyapunov functions for hybrid systems [PDF]

Proceedings of the 24th International Conference on Hybrid Systems: Computation and Control, 2021
We propose a sampling-based approach to learn Lyapunov functions for a class of discrete-time autonomous hybrid systems that admit a mixed-integer representation. Such systems include autonomous piecewise affine systems, closed-loop dynamics of linear systems with model predictive controllers, piecewise affine/linear complementarity/mixed-logical ...
Shaoru Chen, Mahyar Fazlyab, Manfred Morari, George J. Pappas, Victor M. Preciado   +4 more
openaire   +2 more sources

Lyapunov Function and Exponential Trichotomy on Time Scales

Discrete Dynamics in Nature and Society, 2011
We study the relation between Lyapunov function and exponential trichotomy for the linear equation 𝑥Δ=𝐴(𝑡)𝑥 on time scales. Furthermore, as an application of these results, we give the roughness of exponential trichotomy on time scales.
Ji Zhang
doaj   +1 more source

Large-Signal Stability Modeling for the Grid-Connected VSC Based on the Lyapunov Method

Energies, 2018
In this paper, a Lyapunov-based method is used in order to determine the stability boundaries of the grid-connected voltage source converter (VSC). To do so, a state space model of the VSC is used to form the Lyapunov function of the system.
Bahram Shakerighadi, Esmaeil Ebrahimzadeh, Frede Blaabjerg, Claus Leth Bak   +3 more
doaj   +1 more source

Numerical Methods That Preserve a Lyapunov Function for Ordinary Differential Equations

Mathematics, 2022
The paper studies numerical methods that preserve a Lyapunov function of a dynamical system, i.e., numerical approximations whose energy decreases, just like in the original differential equation.
Yadira Hernández-Solano, Miguel Atencia
doaj   +1 more source

Lyapunov Function based Criteria for Ship Rolling in Random Beam Seas

Polish Maritime Research, 2019
The aim of this study is to present a Lyapunov function which can be used to derive an intact stability criterion for a ship in random beam seas. First, the mathematical model of the rolling motion of ships in random beam seas is introduced.
Üçer Erdem
doaj   +1 more source

Mathematical modelling of branched hydraulic systems [PDF]

Компьютерные исследования и моделирование, 2009
Solving the problem of stationary stream distribution for an arbitrary volume-free hydrosystem with a free level can be reduced to determining the extremes of a multi-variable function.
N. V. Kassina, L. V. Smirnov
doaj   +1 more source