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Convergence of an algorithm for constructing Lyapunov functions for switched systems using meshfree collocation
Jay Ward, Nicos Georgiou, Peter Giesl
Switched systems are a class of dynamical systems where trajectories switch between different systems based on a switching rule. This rule can depend on time and/or the position of…
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…
On a matrix-valued PDE characterizing a contraction metric for a periodic orbit
Peter Giesl
The stability and the basin of attraction of a periodic orbit can be determined using a contraction metric, i.e., a Riemannian metric with respect to which adjacent solutions contr…
Converse theorem on a contraction metric for a periodic orbit
Peter Giesl
Contraction analysis uses a local criterion to prove the long-term behaviour of a dynamical system. A contraction metric is a Riemannian metric with respect to which the distance b…
Approximation of Lyapunov Functions from Noisy Data
Peter Giesl, Boumediene Hamzi, Martin Rasmussen +1
Methods have previously been developed for the approximation of Lyapunov functions using radial basis functions. However these methods assume that the evolution equations are known…
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…