5 papers · 1 filter
Review on contraction analysis and computation of contraction metrics
Peter Giesl, Sigurdur Hafstein, Christoph Kawan
Contraction analysis considers the distance between two adjacent trajectories. If this distance is contracting, then trajectories have the same long-term behavior. The main advanta…
Existence of complete Lyapunov functions with prescribed orbital derivative
Peter Giesl, Sigurdur Hafstein, Stefan Suhr
Complete Lyapunov functions for a dynamical system, given by an autonomous ordinary differential equation, are scalar-valued functions that are strictly decreasing along orbits out…
Computation and verification of contraction metrics for exponentially stable equilibria
Peter Giesl, Sigurdur Hafstein, Iman Mehrabinezhad
The determination of exponentially stable equilibria and their basin of attraction for a dynamical system given by a general autonomous ordinary differential equation can be achiev…
Numerical approximation of the data-rate limit for state estimation under communication constraints
Sigurdur Hafstein, Christoph Kawan
In networked control, a fundamental problem is to determine the smallest capacity of a communication channel between a dynamical system and a controller above which a prescribed co…
Construction of a CPA contraction metric for periodic orbits using semidefinite optimization
Peter Giesl, Sigurdur Hafstein
A Riemannian metric with a local contraction property can be used to prove existence and uniqueness of a periodic orbit and determine a subset of its basin of attraction. While the…