An element s of an (abstract) algebra A is a single element of A if asb = 0 and a, b ∈ A imply that as = 0 or sb = 0. Let X be a real or complex reflexive Banach space, and let B be a finite atomic Boolean subspace lattice on X, with the property that the vector sum K +L is closed, for every K,L ∈ B. For any subspace lattice D ⊆ B the single elements of Alg D are characterised in terms of a coo...

In this paper we present a general framework for closed-loop subspace system identi cation. This framework consists of two new projection theorems which allow the extraction of nonsteady state Kalman lter states and of system related matrices directly from closed-loop input output data. Three algorithms for the identi cation of the state space matrices are then presented. The similarities betwe...

So called subspace methods for direct identiication of linear models in state space form have drawn considerable interest recently. They have been found to work well in many cases but have one drawback { they do not yield consistent estimates for data collected under output feedback. This contribution points to the reasons for this and also shows how to modify the basic algorithm to handle clos...

This paper deals with the problem of continuoustime model identification and presents a subspace-based algorithm capable of dealing with data generated by systems operating in closed-loop. The algorithm is developed by reformulating the identification problem from the continuous-time model to an equivalent one to which discrete-time subspace identification techniques can be applied. More precis...

We introduce a weakened version of the Dunford-Pettis property, and give examples of Banach spaces with this property. In particular, we show that every closed subspace of Schreier’s space S enjoys it. As an application, we characterize the weak polynomial convergence of sequences, show that every closed subspace of S has the polynomial Dunford-Pettis property of Biström et al. and give other p...

Closed-loop system identification and fault detection and isolation are the two fundamental building blocks of process monitoring. Efficient and accurate process monitoring increases plant availability and utilisation. This dissertation investigates a subspace system identification and fault detection methodology for the Benfield process, used by Sasol, Synfuels in Secuda, South Africa, to remo...

The purpose of this thesis was to investigate how different subspace identification methods cope with closed loop data, and how the controller parameters affect the quality of the acquired models. Three different subspace methods were subject for investigation; the MOESPmethod, theN4SIDmethod and theDSR_emethod. It is shown through a simulation example that all three subspace methods will ident...

We show that the space Lip0(R) is the dual space of L(R;R)/N where N is the subspace of L(R;R) consisting of vector fields whose divergence vanishes identically. We prove that although the quotient space L(R;R)/N is weakly sequentially complete, the subspace N is not nicely placed in other words, its unit ball is not closed for the topology τm of local convergence in measure. We prove that if Ω...

Precise conditions are given under which the real interpolation space [Y0, X1]θ,p coincides with a closed subspace of [X0,X1]θ,p when Y0 is a closed subspace of codimension one. This result is applied to the study of nonharmonic Fourier series in the Sobolev spaces Hs(−π, π) with 0 < s < 1. The main result looks like this: if {eiλnt} is an unconditional basis in L2(−π, π), then there exist two ...