In this paper two disturbance decoupling problems without stability and with quadratic stability via dynamic output feedback for switched linear systems are investigated. Firstly, simultaneous (C,A,B)-pair which incorporates both the concept of simultaneous (A,B)-invariant subspace and its dual simultaneous (C,A)-invariant subspace for a family of linear systems are investigated. Secondly, dist...

We are interested in the following problem: to describe the closed translation-invariant subspaces of lp(Z). For l2 there is a complete solution due to Wiener, in terms of zeros of Fourier transform. However, the situation when p 6= 2 is much harder. In this talk we will present a proof of Malliavin’s theorem which shows the difficulty of characterizing all invariant subspaces of l1. We will us...

Subspace methods such as MUSIC, Minimum Norm, and ESPRIT have gained considerable attention due to their superior performance in sinusoidal and direction-of-arrival (DOA) estimation, but they are also known to be of high computational cost. In this paper, new fast algorithms for approximating signal and noise subspaces and that do not require exact eigendecomposition are presented. These algori...

In this paper, subspace identification for wind turbines and more generally rotating periodic systems are investigated. Previous works have stressed the difficulty of modeling such as Linear Time Invariant thus to apply classical Stochastic Subspace Identification. Such plead or augmented theories. SSI can be applied recover modal information that is related eigenstructure instrumented system d...

In this report, a summary of [1] is given. In [1] the authors provide a complete characterization of closed shift-invariant subspaces of L2(R) and the corresponding approximation order. The characterization of principal shift-invariant spaces is given in terms of the Fourier transform of the generator. The approximation order of a general shift-invariant space is the same as a suitably chosen p...

This report describes an idea based on the work in [1], where an algorithm for learning automatic representation of visual operators is presented. The algorithm in [1] uses canonical correlation to find a suitable subspace in which the signal is invariant to some desired properties. This report presents a related approach specially designed for classification problems. The goal is to find a sub...

Let $H$ and $K$ be compact subgroups of locally compact group $G$. By considering the double coset space $Ksetminus G/H$, which equipped with an $N$-strongly quasi invariant measure $mu$, for $1leq pleq +infty$, we make a norm decreasing linear map from $L^p(G)$ onto $L^p(Ksetminus G/H,mu)$ and demonstrate that it may be identified with a quotient space of $L^p(G)$. In addition, we illustrate t...

Vanderbauwhede and van Gils, Krupa, and Langford studied unfoldings of bifurcations with purely imaginary eigenvalues and a nonsemisimple linearization, which generically occurs in codimension three. In networks of identical coupled ODE these nilpotent Hopf bifurcations can occur in codimension one. Elmhirst and Golubitsky showed that these bifurcations can lead to surprising branching patterns...

The most expensive part of all electronic structure calculations based on density functional theory lies in the computation of an invariant subspace associated with some of the smallest eigenvalues of a discretized Hamiltonian operator. The dimension of this subspace typically depends on the total number of valence electrons in the system, and can easily reach hundreds or even thousands when la...

The most expensive part of all Electronic Structure Calculations based on Density Functional Theory, lies in the computation of an invariant subspace associated with some of the smallest eigenvalues of a discretized Hamiltonian operator. The dimension of this subspace typically depends on the total number of valence electrons in the system, and can easily reach hundreds or even thousands when l...