Une fonction scalaire V(x) continue et différenciable sur un voisinage U de xe, est 0 ∀ ∈ D fonction de Lyapunov stricte pour. Boundedness and Lyapunov function for a nonlinear system of hematopoietic stem cell dynamicsSolutions bornées et fonction de Lyapunov pour un système. Dans cette Note on propose une nouvelle fonction de Lyapunov pour l’étude de la stabilité asymptotique globale dans un modèle mathématique de compétition.

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For an iISS dynamic system with perturbation, we introduce an auxiliary system which is uniformly asymptotically stable.

The proposed method constructs a continuous and piecewise affine CPA function fonctioon a compact subset of state space with the origin in its interior based on functions from classical converse Lyapunov theorems originally due to Yoshizawa, and then verifies if the vertex values satisfy linear inequalities for vertices in the subset excluding a small neighborhood of the origin. For each subsystem, an ISS Lyapunov function foction computed by our proposed method.

This page was last edited on 6 Octoberat We further state that the iISS Lyapunov function is a local input to state stable ISS Lyapunov function for the considered dynamic system with perturbations on a subset of the domain of attraction for the auxiliary system.

Wikipedia articles incorporating text from PlanetMath. Since a maximal robust Lyapunov function for uniformly lyapunog stable systems can be obtained using Zubov’s ffonction, we present a new way of computing integral input-to- state stable iISS Lyapunov functions by Zubov’s method and auxiliary systems in Chapter 3. University of Bayreuth, Monday, June 8, – 5: Then a robust Lyapunov function for the auxiliary system is computed by Zubov’s method.

An academic example is shown to illustrate how this method is applied.

Saturday, March 7, – A Lyapunov function for an autonomous dynamical system. By using this site, you agree to the Terms of Use and Privacy Policy. Stability of the interconnected systems is then analyzed by the small gain theorem in comparison form and the small gain theorem in dissipative form, respectively. In order to analyse stability of interconnected systems in Chapters 3 and 4, we lyaapunov three small gain theorems.

### Lyapunov function – Wikipedia

For certain classes of ODEs, the existence of Lyapunov functions is a necessary and sufficient condition for stability. Huijuan Li 1 Details. We propose a new approach of computing Lyapunov functions for dynamic systems without perturbations with an asymptotically stable equilibrium at the origin in Chapter 2.

In the theory of ordinary differential equations ODEsLyapunov functions are scalar functions that may be used to prove the stability of an equilibrium of an ODE.

## Lyapunov function

Huijuan Li 1 AuthorId: Whereas there is no general technique for constructing Lyapunov functions for ODEs, in many specific cases the construction of Lyapunov functions is known. In this thesis, we investigate the problems of computation of Lyapunov functions and stability analysis of interconnected systems. By the chain rule, for any function, H: Furthermore, we study stability of interconnected ISS systems.

For instance, quadratic functions suffice for systems with one state; the solution of a particular linear matrix inequality provides Lyapunov functions for linear systems; and conservation laws can often be used to construct Lyapunov functions for physical systems. Optimization and Control [math. Since the interpolation errors are incorporated in the linear constraints, as in Chapter 2 the computed ISS Lyapunov function is a true ISS Lyapunov function rather than a numerical approximation.

A similar concept appears in the theory of general state space Markov chainsusually under the name Foster—Lyapunov functions.

We prove that the linear optimization lypunov has a feasible solution if the system is ISS. In Chapter 4, we design a numerical algorithm for computing ISS Lyapunov functions for dynamic systems with perturbations.

If the linear inequalities are satisfied, then the CPA function is a CPA Lyapunov function on the subset excluding a small neighborhood of the origin.

Have you forgotten your login? The converse is also true, and was proved by J. In Chapter 1, preliminary results about stability, definitions of Lyapunov functions and lyqpunov are presented.

Note that using the same Lyapunov candidate one can show that the equilibrium is also globally asymptotically stable. Retrieved from ” https: From Wikipedia, the free encyclopedia.