TEOREMA DE LYAPUNOV- DEMOSTRACIÓN. BÚSQUEDA DE FUNCIONES DE LYAPUNOV. BÚSQUEDA DE FUNCIONES DE LYAPUNOV. BÚSQUEDA. This MATLAB function solves the special and general forms of the Lyapunov equation. funciones de Lyapunov; analisis númerico. 1 Introduction. The synchronization of electrical activity in the brain occurs as the result of interaction among sets of.

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This model is so-called AR Auto Regressive model.

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Lyapunov functions arise in the study of equilibrium points of dynamical systems. In the Funcionrs transformation, the time-shift operator is described as where is the sampling period for simplicity, and without loss of generality, is assumed. The candidate Lyapjnov function is given by: In the first, for the simulation example, the real system model is assumed to be represented by: In order to derive the nominal control law the polynomials and are assumed to have constant and known parameters, represented by: The degree of polynomial iswhich implies that depends only on future states of x.

Whereandare the upper and lower bounds of andrespectively.

Lyapunov function

This page has been translated by MathWorks. The initial condition where I is the identity matrix and the parameter forgetting factor are chosen.


Based on your location, we recommend that you select: Estabilidad de controladores auto-ajustables para sistemas variantes en el tiempo basada en funciones Lyapunov. Translated by Mouseover text to see original. However, all these researches have been done for time-invariant systems TIS. The A matrix is stable, and the Q matrix is positive definite. MathWorks does not lyapubov, and disclaims all liability for, the accuracy, suitability, or fitness for purpose of the translation.

Description lyap solves the special and general forms of the Lyapunov equation. The proposed algorithm is extended to the case where system and measurement noises are considered.

The white noise signal is defined as a bounded independent random sequence, which has the following properties: If the control law in Eq. A similar concept appears in the theory of general state space Markov chainsusually under the name Foster—Lyapunov functions.

Lyapunov function – Wikipedia

dunciones Then, for dee, the following is derived: By the chain rule, for any function, H: For certain classes of ODEs, the existence of Lyapunov functions is a necessary and sufficient condition for stability.

The polynomial is chosen Schur and should be designed by assigning all characteristic roots inside the unit disk in the z-plane. Solution does not exist or is not unique. For robust stability analysis, we may use the method by Tsypkin [10] for closed-loop discrete-time systems, which involves the modified characteristic locus criterion.


The results have been extended to the case where system and measurement noises are considered into the system model.

Then, the family lyqpunov system models is represented by: Equation 31 implies that approaches to zero as N goes to infinity; then the left-hand side of Eq. We do not prove, or claim, that converges to its true values q. From the third term on the right-hand side of Eq.

A Lyapunov function for an autonomous dynamical system. Figure 2 shows the output responses when, after samples, the system model in Eq. Views Read Edit View history. Funcioes there is no general technique for constructing Lyapunov functions for ,yapunov, in many specific cases the construction of Lyapunov functions is known.

Select a Web Site Choose a web site to get translated content where available and see local events and offers. Then, for a large N the following relation is derived: