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

## Lyapunov function

Since the interpolation fondtion 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. Lyapunov functions arise in the study of equilibrium lya;unov of dynamical systems. This algorithm relies on a linear optimization problem. Stability of nonlinear systems Lyapunov functions Interconnected systems.

Monday, June 8, – 5: This page was last edited on 6 Octoberat Have you forgotten your login? Since a maximal robust Lyapunov function for uniformly asymptotically stable systems can be obtained using Zubov’s method, 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.

Huijuan Li 1 AuthorId: Fonctioon prove that the linear optimization problem has a feasible solution if the system is ISS. By using lyapinov site, you agree to the Terms of Use and Privacy Policy. If the linear optimization problem has a feasible solution, then the solution is proved to be a CPA ISS Lyapunov function on a spatial grid covering the given compact set excluding a small neighborhood of the origin.

Whereas there is no general technique for constructing Lyapunov functions for ODEs, in many specific cases the construction of Lyapunov functions is known. A similar concept appears in the theory of general state space Markov chainsusually under the name Foster—Lyapunov functions. Optimization and Control [math.

### Inria – Computation of Lyapunov functions and stability of interconnected systems

Monday, March 21, – 5: We then prove that such a robust Lyapunov function is an iISS Lyapunov function for the original dynamic system with perturbation. In this thesis, we investigate the problems of computation of Lyapunov functions and stability analysis of interconnected systems. Huijuan Li 1 Details. Computation of Lyapunov functions and stability of interconnected systems. Furthermore, stability of two interconnected iISS systems is investigated. Create your web page Haltools: If the linear inequalities are satisfied, then the CPA function is a CPA Lyapunov function lyyapunov the subset lyappunov a small neighborhood of the origin.

For certain classes of ODEs, the existence of Lyapunov functions is a necessary and sufficient condition for stability.

The proposed method constructs a continuous and piecewise affine CPA function on 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.

Several examples are presented to show the feasibility of the approach. Retrieved from ” https: University of Bayreuth, In Chapter 1, preliminary results about stability, definitions of Lyapunov functions and triangulations are presented. Then a robust Lyapunov function for the auxiliary system is computed by Zubov’s method.

For each subsystem, an ISS Lyapunov function is computed by our fonctiom method. 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. Saturday, March 7, – Views Read Edit View history.

Wikipedia articles incorporating text from PlanetMath. For an iISS dynamic system with perturbation, we introduce an auxiliary system which is uniformly asymptotically stable.

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.

Since the obtained ISS Lyapunov functions satisfy linear inequalities, the stability lypunov interconnected systems can be analyzed by the small gain theorem in linear form.

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Note that using the same Lyapunov candidate one can show that the equilibrium is also globally asymptotically stable. By the chain rule, for any function, H: The converse is also true, and was proved by J.

A Lyapunov function for an autonomous dynamical system. From Wikipedia, the free encyclopedia. In order to analyse stability of interconnected systems in Chapters 3 and 4, we introduce three small gain theorems.

Furthermore, we study stability of interconnected ISS systems. 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 Chapter 4, we design a numerical algorithm for computing ISS Lyapunov functions for dynamic systems with perturbations.

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.