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.

By using this site, you agree to the Terms of Use and Privacy Policy. The converse is also true, and was proved by J. We prove that the linear optimization problem has a feasible solution if the system is ISS.

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Since the interpolation errors are incorporated in the linear constraints, as in Chapter 2 the lyapujov ISS Lyapunov function is a true ISS Lyapunov function rather than a numerical approximation.

Then a robust Lyapunov function for the auxiliary system is computed by Zubov’s method. Wikipedia articles incorporating text from PlanetMath. This page was last edited on 6 Octoberat 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.

Retrieved from ” https: 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.

Huijuan Li 1 AuthorId: Lyapunov functions arise in the study of equilibrium points of dynamical systems. 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.

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

Monday, June 8, – 5: Create your web page Haltools: Views Read Edit View history. 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.

We then prove that such a robust Lyapunov function is an iISS Lyapunov function for the original dynamic system with perturbation. Stability of nonlinear systems Lyapunov functions Interconnected systems. 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.

Note that using the same Lyapunov candidate one can show that the equilibrium is also globally asymptotically stable.

## Lyapunov function

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 Lyapuhov functions and stability analysis of interconnected systems.

This algorithm relies on a linear optimization problem. By the chain rule, for any function, H: Monday, March 21, – 5: From Wikipedia, the free encyclopedia.

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

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

For an iISS dynamic system with perturbation, we introduce an auxiliary system which is uniformly asymptotically stable. In order to analyse stability of interconnected systems in Chapters 3 and 4, we introduce three small gain theorems.