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- Peter Giesl
- 2014

In this paper, we derive error estimates for generalized interpolation, in particular collocation, in Sobolev spaces. We employ our estimates to collo-cation problems using radial basis functions and extend and improve previously known results for elliptic problems. Finally, we use meshless colloca-tion to approximate Lyapunov functions for dynamical… (More)

- Peter Giesl, Sigurdur Hafstein
- 2015

Lyapunov functions are an essential tool in the stability analysis of dynamical systems, both in theory and applications. They provide sufficient conditions for the stability of equilibria or more general invariant sets, as well as for their basin of attraction. The necessity, i.e. the existence of Lyapunov functions, has been studied in converse theorems,… (More)

- Najla Mohammed, Peter Giesl
- 2015

Lyapunov functions are a main tool to determine the domain of attraction of equilibria in dynamical systems. Recently, several methods have been presented to construct a Lyapunov function for a given system. In this paper , we improve the construction method for Lyapunov functions using Radial Basis Functions. We combine this method with a new grid… (More)

- Peter Giesl
- 2014

The stability and basin of attraction of an equilibrium can be determined by a contraction metric. A contraction metric is a Riemannian metric with respect to which the distance between adjacent trajectories decreases. The advantage of a contraction metric over, e.g., a Lyapunov function is that the contraction condition is robust under perturbations of the… (More)

— The numerical construction of Lyapunov functions provides useful information on system behavior. In the Continuous and Piecewise Affine (CPA) method, linear programming is used to compute a CPA Lyapunov function for continuous nonlinear systems. This method is relatively slow due to the linear program that has to be solved. A recent proposal was to… (More)

— An integral part of the CPA method to compute Continuous and Piecewise Affine Lyapunov functions for nonlinear systems is the generation of a suitable triangulation. Recently, the CPA method was revised by using more advanced triangulations and it was proved that it can compute a CPA Lya-punov function for any nonlinear system possessing an exponentially… (More)

Fast periodic motions of robots can be open-loop stable or self-stabilizing if all the model parameters of the robot, like masses, geometric properties, springs, dampers etc. as well the torques and forces driving the motion are carefully adjusted and selected exploting the inherent dynamic properties of the mechanical system. Biological systems exhibit… (More)

- Jóhann Björnsson, Peter Giesl, Sigurdur F Hafstein, Christopher M Kellett
- 2015

We present a novel method to compute Lyapunov functions for continuous-time systems with multiple local attractors. In the proposed method one first computes an outer approximation of the local attractors using a graph-theoretic approach. Then a candidate Lyapunov function is computed using a Massera-like construction adapted to multiple local attractors.… (More)