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Approximate tracking and disturbance rejection for stable infinite-dimensional systems using sampled-data low-gain control
In this paper we solve tracking and disturbance rejection problems for stable infinite-dimensional systems using a simple low-gain controller suggested by the internal model principle. For stable discrete-time systems, it is...
Nonexistence of slow heteroclinic travelling waves for a bistable Hamiltonian lattice model
The nonexistence of heteroclinic travelling waves in an atomistic model for martensitic phase transitions is the focus of this study. The elastic energy is assumed to be piecewise quadratic, with two wells representing two...
Infinite-dimensional Lur'e systems
We consider forced Lur'e systems in which the linear dynamic component is an infinite-dimensional well-posed system. Numerous physically motivated delay- and partial differential equations are known to belong to this class of...
A circle criterion for strong integral input-to-state stability
We present sufficient conditions for integral input-to-state stability (iISS) and strong iISS of the zero equilibrium pair of continuous-time forced Lur'e systems, where by strong iISS we mean the conjunction of iISS and...
Stabilization of well-posed infinite-dimensional systems by dynamic sampled-data feedback
Hartmut Logemann
Jan 01, 0001
It is shown that a set of six natural conditions is necessary and sufficient for the existence
of a finite-dimensional stabilizing sampled-data controller for a well-posed infinite-dimensional
system. The underlying...
of a finite-dimensional stabilizing sampled-data controller for a well-posed infinite-dimensional
system. The underlying...
Minimizers of a weighted maximum of the Gauss curvature
On a Riemann surface [`(S)] with smooth boundary, we consider Riemannian metrics conformal to a given background metric. Let κ be a smooth, positive function on [`(S)]. If K denotes the Gauss curvature, then the L ∞-norm of K/κ...
Approximate tracking and disturbance rejection for stable infinite-dimensional systems using sampled-data low-gain control
In this paper we solve tracking and disturbance rejection problems for stable infinite-dimensional systems using a simple low-gain controller suggested by the internal model principle. For stable discrete-time systems, it is...
The Circle Criterion and Input-to-State Stability
This article provides an overview of the circle criterion and its connection with ISS. Classical absolute stability theory and the circle criterion in particular, is concerned with the analysis of a feedback interconnection of...
Minimizers of a weighted maximum of the Gauss curvature
On a Riemann surface [`(S)] with smooth boundary, we consider Riemannian metrics conformal to a given background metric. Let κ be a smooth, positive function on [`(S)]. If K denotes the Gauss curvature, then the L ∞-norm of K/κ...
A sampled-data servomechanism for stable well-posed systems
In this technical note, an approximate tracking and disturbance rejection problem is solved for the class of exponentially stable well-posed infinite-dimensional systems by invoking a simple sampled-data low-gain controller...
A sampled-data servomechanism for stable well-posed systems
In this technical note, an approximate tracking and disturbance rejection problem is solved for the class of exponentially stable well-posed infinite-dimensional systems by invoking a simple sampled-data low-gain controller...
Travelling waves for a Frenkel-Kontorova chain
In this article, the Frenkel–Kontorova model for dislocation dynamics is considered, where the on-site potential consists of quadratic wells joined by small arcs, which can be spinodal (concave) as commonly assumed in physics....
Absolute stability and integral control for infinite-dimensional discrete-time systems
We derive absolute stability results of Popov and circle-criterion types for infinite-dimensional discrete-time systems in an input-output setting. Our results apply to feedback systems in which the linear part is the series...
Calculation of long time classical trajectories
We study the problem of finding a path that joins a given initial state with a final one, where the evolution is governed by classical (Hamiltonian) dynamics. A new algorithm for the computation of long time transition...
Kinetic relations for a lattice model of phase transitions
The aim of this article is to analyse travelling waves for a lattice model of phase transitions, specifically the Fermi-Pasta-Ulam chain with piecewise quadratic interaction potential. First, for fixed, sufficiently large...
Semi-global incremental input-to-state stability of discrete-time Lur’e systems
We present sufficient conditions for semi-global incremental input-to-state stability of a class of forced discrete-time Lur'e systems. The results derived are reminiscent of well-known absolute stability criteria such as the...
Indirect sampled-data control with sampling period adaptation
It is known that if a continuous-time feedback system is exponentially stable, then the corresponding sampled-data system obtained by sample-hold discretisation with constant sampling period is also exponentially stable...
Absolute stability and integral control for infinite-dimensional discrete-time systems
We derive absolute stability results of Popov and circle-criterion types for infinite-dimensional discrete-time systems in an input-output setting. Our results apply to feedback systems in which the linear part is the series...
A circle criterion for strong integral input-to-state stability
We present sufficient conditions for integral input-to-state stability (iISS) and strong iISS of the zero equilibrium pair of continuous-time forced Lur'e systems, where by strong iISS we mean the conjunction of iISS and...
Kinetic relations for a lattice model of phase transitions
The aim of this article is to analyse travelling waves for a lattice model of phase transitions, specifically the Fermi-Pasta-Ulam chain with piecewise quadratic interaction potential. First, for fixed, sufficiently large...
Input-to-state stability of discrete-time Lur'e systems
An input-to-state stability theory, which subsumes results of circle criterion type, is
developed in the context of discrete-time Lur’e systems. The approach developed is inspired by the complexified Aizerman conjecture.
developed in the context of discrete-time Lur’e systems. The approach developed is inspired by the complexified Aizerman conjecture.
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