We develop a closed loop subspace identification method based on stochastic realization theory. Using the preliminary orthogonal decomposition of (Picci and Katayama, 1996b) we show that, under the assumption that the exogenous input is feedback-free and persistently exciting (PE), the identification of closed loop systems is divided into two subproblems: the deterministic identification of the...

Johnson and Zippin recently showed that ifX is a weak∗-closed subspace of l1 and T : X → C(K) is any bounded operator then T can extended to a bounded operator T̃ : l1 → C(K). We give a converse result: if X is a subspace of l1 so that l1/X has a (UFDD) and every operator T : X → C(K) can be extended to l1 then there is an automorphism τ of l1 so that τ(X) is weak∗-closed. This result is proved ...

In this paper, we consider a closed-loop subspace identification problem without using probing inputs; but we assume that there is a measurable disturbance which can be used as a test input for identification. Deterministic and stochastic subsystems are derived by applying the orthogonal decomposition (ORT) of the joint input-output process and realization methods. We develop a new ORTbased clo...

When data is sampled from an unknown subspace, principal component analysis (PCA) provides an effective way to estimate the subspace and hence reduce the dimension of the data. At the heart of PCA is the EckartYoung-Mirsky theorem, which characterizes the best rank k approximation of a matrix. In this paper, we prove a generalization of the Eckart-Young-Mirsky theorem under all unitarily invari...

More cost-effective wind turbines with higher rated power, are desired to emerge in the near future. The current trend in wind energy is for this reason the increase of the wind turbine dimensions. Increasing their size is however strongly limited by the rotor blades structural integrity towards occurring aeroelastic loads, especially with respect to blade fatigue. Advanced (re)active load redu...

If a separable Banach space X is such that for some nonquasireflexive Banach space Y there exists a surjective strictly singular operator T : X → Y then for every countable ordinal α the dual of X contains a subspace whose weak∗ sequential closures of orders less than α are not norming over any infinite-dimensional subspace of X and whose weak∗ sequential closure of order α+ 1 coincides with X∗...

Based on the Krylov-Bogolyubov method of averaging the closed system of equations for particle motion and temperature in inhomogeneous rapidly oscillating velocity and temperature of fluid phase is derived. It is shown that the particle movement in a rapidly oscillating fluid velocity field occurs not only under the force of gravity and resistance, but also under force of migration. The migrati...

We show that a separable proximinal subspace of X, say Y is strongly proximinal (strongly ball proximinal) if and only if Lp(I, Y ) is strongly proximinal (strongly ball proximinal) in Lp(I,X), for 1 ≤ p <∞. The p =∞ case requires a stronger assumption, that of ’uniform proximinality’. Further, we show that a separable subspace Y is ball proximinal in X if and only if Lp(I, Y ) is ball proximin...

We consider the problem of delay estimation in an asyn-chronous wireless CDMA communication system. The received observations are decomposed into orthogonal signal and noise subspaces via the singular value decomposition (SVD). A class of techniques known as subspace tting techniques is used to estimate the individual user delays by maximizingthe t between the signal subspace and the observed d...

Let X,Y be normed spaces. The set of bounded linear operators is noted as L(X,Y ). Let now D = D(A) ⊂ X be a linear subspace, and A : D −→ Y a linear (not necessarily bounded!) operator. Notation: (A,D(A)) : X −→ Y Definition: G(A) := {(x,Ax) |x ∈ D} is called the graph of A. Obviously, G(A) is a linear subspace of X × Y . The linear operator A is called closed if G(A) is closed in X × Y . The ...