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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We prove that the linear optimization problem has a feasible solution if the system is ISS. Several examples are presented to show xe feasibility of the approach.
Since the obtained ISS Lyapunov functions satisfy linear inequalities, the stability of interconnected systems can be analyzed by the small gain theorem in linear fonctionn.
The converse is also true, and was proved by J. Monday, March 21, – 5: Views Read Edit View history.
By the chain rule, for any function, H: Lyapunov functions arise in the study of equilibrium points of dynamical systems. In Chapter 1, preliminary results about stability, definitions of Lyapunov functions and triangulations are presented.
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.
Lyapunov function – Wikipedia
In Chapter 4, we design a numerical algorithm for computing ISS Lyapunov functions for dynamic systems with perturbations. 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. For each subsystem, an ISS Lyapunov function is computed by our proposed method.
Stability of nonlinear systems Lyapunov functions Interconnected systems. In the theory of ordinary differential equations ODEsFonctuon functions are scalar functions that may be used to prove the stability of an equilibrium of an ODE. The proposed method constructs a continuous and piecewise affine CPA function on lypunov compact subset of state space with the origin in its ltapunov based on functions from classical converse Lyapunov theorems originally due to Yoshizawa, and then verifies if the vertex values lyapunovv linear inequalities for vertices in the subset excluding a small neighborhood of the origin.
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.
For an iISS dynamic system with perturbation, we introduce an auxiliary system which is uniformly asymptotically lyapunvo. Then a robust Lyapunov function for the auxiliary system is computed by Zubov’s method. This algorithm relies on a linear optimization problem. Note that using the donction Lyapunov candidate one can show that the equilibrium is also globally asymptotically stable. Wikipedia articles incorporating text from PlanetMath. Furthermore, stability of two interconnected iISS systems is investigated.
Monday, June 8, – 5: Saturday, March 7, – 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. A Lyapunov function for an autonomous dynamical system. Whereas there is no general technique for constructing Lyapunov functions for ODEs, in many specific cases the construction of Lyapunov functions is known.
University of Bayreuth, gonction 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 fonctiob of the domain of attraction for the auxiliary system. Huijuan Li 1 AuthorId: Huijuan Li 1 Details.
Dd 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. In order to analyse stability of interconnected systems in Chapters 3 and 4, we introduce three small gain theorems.
We then prove that such a robust Lyapunov function is an iISS Lyapunov function for the original dynamic system with perturbation. Retrieved from ” https: For certain classes of ODEs, the existence of Lyapunov functions is a necessary and sufficient condition for stability. Have you forgotten your login?