#### FONCTION DE LYAPUNOV PDF

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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Then a robust Lyapunov function for the auxiliary system is computed by Zubov’s method. A Lyapunov function for an autonomous dynamical system. We further state that the iISS Lyapunov function is a local input to state stable ISS Lyapunov function lya;unov the considered dynamic system with perturbations on a subset of the domain of attraction for the auxiliary system.

## Lyapunov function

A similar concept appears in the theory of general state space Markov chainsusually under the name Foster—Lyapunov functions. Note that using the same Lyapunov candidate one can show that the equilibrium is also globally asymptotically stable. Have you forgotten your login? University of Bayreuth, 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.

Wikipedia articles incorporating text from PlanetMath. Computation of Lyapunov functions and stability of interconnected systems. Lyaupnov Wikipedia, the free encyclopedia.

For an iISS dynamic system with perturbation, we introduce an auxiliary system which is uniformly asymptotically stable. Whereas there is no general technique for constructing Lyapunov functions for ODEs, in many specific cases the construction of Lyapunov functions is known. In Chapter 4, we design a numerical algorithm for computing ISS Lyapunov functions for dynamic systems with perturbations.

Optimization and Control [math. Several examples are presented to show the feasibility of the approach.

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

In Chapter 1, preliminary results about stability, definitions of Lyapunov functions and triangulations are presented. For each subsystem, an ISS Lyapunov function is computed by our proposed method. 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. Create your web page Haltools: This algorithm relies on a linear optimization problem.

Furthermore, stability of two interconnected iISS systems is investigated. Since the fonctoon 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.

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

lyapuno Since a maximal robust Lyapunov function for uniformly asymptotically stable systems can be obtained using Fonctin 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. 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.

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By the chain rule, for any function, H: Monday, June 8, – 5: The proposed method constructs a continuous and piecewise affine CPA function on a lyapynov 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 re the subset excluding a small neighborhood of the origin.

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.

Stability of nonlinear systems Lyapunov functions Interconnected systems. 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 oyapunov Chapter 2.

Furthermore, lyapuno study stability of interconnected ISS systems. We prove that the linear optimization problem has a feasible solution if the system is ISS. Saturday, March 7, – Since the obtained ISS Lyapunov functions satisfy linear inequalities, the stability of interconnected systems can be analyzed by the small gain theorem in linear form. By using this site, you agree to the Terms of Use and Privacy Policy.