Results 1 to 10 of about 6,993 (196)

Control Lyapunov Functions and Zubov's Method [PDF]

SIAM Journal on Control and Optimization, 2008
For finite dimensional nonlinear control systems we study the relation between asymptotic null-controllability and control Lyapunov functions. It is shown that control Lyapunov functions may be constructed on the domain of asymptotic null-controllability as viscosity solutions of a first order PDE that generalizes Zubov's equation. The solution is also
CAMILLI, FABIO, L. Gruene, Fabian Wirth
openaire   +3 more sources

Computational methods for Lyapunov functions

Discrete and Continuous Dynamical Systems - Series B, 2015
Lyapunov functions, introduced by Lyapunov more than 100 years ago, are to this day one of the most important tools in the stability analysis of dynamical systems. They are functions which decrease along solution trajectories of systems, and they can be used to show stability of an invariant set, such as an equilibrium, as well as to determine its ...
Peter Giesl, Sigurdur Hafstein
openaire   +1 more source

A Survey of Quantum Lyapunov Control Methods [PDF]

The Scientific World Journal, 2013
The condition of a quantum Lyapunov‐based control which can be well used in a closed quantum system is that the method can make the system convergent but not just stable. In the convergence study of the quantum Lyapunov control, two situations are classified: nondegenerate cases and degenerate cases.
Shuang Cong, Fangfang Meng
openaire   +4 more sources

DESCRIPTOR DISCRETIZED LYAPUNOV FUNCTIONAL METHOD

IFAC Proceedings Volumes, 2006
Abstract Stability and state-feedback stabilization of linear systems with constant delays are considered. The system under consideration may be unstable without delay, but it becomes asymptotically stable for positive values of the delay. A new descriptor discretized Lyapunov Krasovskii Functional (LKF) method is introduced, which combines the ...
openaire   +1 more source

Variational lyapunov method for discrete hybrid systems

Mathematical and Computer Modelling, 2003
This paper deals with the initial value problem \(\Delta y(n)=f(n,y(n))\), \(y(n_0)=y_0\). In their paper [Appl. Anal. 83, 363--376 (2004; Zbl 1055.39006)], the authors present the nonlinear variation of parameter (NVP) formula. Here they offer its improved version where the smoothness condition on \(f\) with respect to \(y\) is relaxed. In addition, a
Dontha, S., Drici, Z.
openaire   +2 more sources

The Lyapunov spectrum as the Newton method [PDF]

Physica A: Statistical Mechanics and its Applications, 2012
For a class of dynamical systems, the cookie-cutter maps, we prove that the Lyapunov spectrum coincides with the map given by the Newton-Raphson method applied to the derivative of the pressure function.
openaire   +5 more sources

Lyapunov's Second Method for Random Dynamical Systems

Journal of Differential Equations, 2001
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Arnold, Ludwig, Schmalfuss, Björn
openaire   +2 more sources

Classical converse theorems in Lyapunov's second method

Discrete and Continuous Dynamical Systems - Series B, 2015
Lyapunov's second or direct method is one of the most widely used techniques for investigating stability properties of dynamical systems. This technique makes use of an auxiliary function, called a Lyapunov function, to ascertain stability properties for a specific system without the need to generate system solutions.
openaire   +4 more sources

Stable approach based diagonal recurrent quantum neural networks for identification of nonlinear systems. [PDF]

Sci Rep
Khalil H, Elshazly O, Shaheen O.
europepmc   +1 more source

An extension of Lyapunov's direct method.

Michigan Mathematical Journal, 1965
Bhatia, Nam P., Lakshmikantham, V.
openaire   +3 more sources