In this paper, we intend to define and study concepts of weight and weighted spaces of holomorphic (analytic) functions on the upper half plane. We study two special classes of these spaces of holomorphic functions on the upper half plane. Firstly, we prove these spaces of holomorphic functions on the upper half plane endowed with weighted norm supremum are Banach spaces. Then, we investigate t...

Subspace predictive control (SPC) is recently seen in the literature for joint system identification and control design. This combination enables automatically tuning the parameters in conventional model predictive control (MPC); and therefore provides a solution to the problem of fault tolerant MPC design. The existing SPCs either deal with open-loop data or depend on the information of the co...

We propose in this paper a novel subspace identification method, based on PARSIMonious parameterization (Qin et al., 2005), and we show that such algorithm guarantees consistent estimates of the Markov parameters with open-loop and closed-loop data. The method uses the predictor form and it effectively exploits in all steps the Toeplitz structure of the Markov parameters’ matrices. After evalua...

Quantum phenomena of interest in connection with quantum computation and communication often deal with transfers between eigenstates, and their linear superpositions. For systems having only a finite number of states, the quantum evolution equation (the Schrödinger equation) is finite-dimensional and the results on controllability on Lie groups as worked out decades ago [1] provide most of what...

Let H 2 ( D n ) denote the Hardy space over polydisc , ≥ . A closed subspace Q ⊆ is called Beurling quotient module if there exists an inner function θ ∈ ∞ such that = / We present a complete characterization of modules : be subspace, and let C z i P M | 1 … Then only I − ⁎ j 0 ≠ two applications: first, we obtain dilation theorem for Brehmer -tuples commuting contractions, and, second, relate ...

Subspace identification for closed loop systems has been recently studied by several authors. Even though results are available which allows to compute the asymptotic variance of the estimated parameters for several algorithms, less clear is the situation as to relative performance is concerned. In this paper we partly answer this last question showing that the SSARX algorithm introduced by Jan...

In this paper, a closed-loop subspace identification approach through an orthogonal projection and subsequent singular value decomposition is proposed. As a by-product of this development, it explains why some existing subspace methods may deliver a bias in the presence of the feedback control and suggests a remedy to eliminate the bias. Furthermore, as the proposed method is a projection based...

Subspace identification for closed loop systems has been recently studied by several authors. Recent results are available which express the asymptotic variance of the estimated parameters (and hence of any system invariant) as a function of the “true” underlying system parameters and of certain conditional covariance matrices. When it comes to using these formulas in practice one is faced with...

Let A be a bounded self-adjoint operator on a separable Hilbert space H and H0 ⊂ H a closed invariant subspace of A. Assuming that H0 is of codimension 1, we study the variation of the invariant subspace H0 under bounded self-adjoint perturbations V of A that are off-diagonal with respect to the decomposition H = H0 ⊕H1. In particular, we prove the existence of a oneparameter family of dense no...

(i) CAC iff every countable product of sequential metric spaces (sequentially closed subsets are closed) is a sequential metric space iff every complete metric space is Cantor complete. (ii) Every infinite subset X of R has a countably infinite subset iff every infinite sequentially closed subset of R includes an infinite closed subset. (iii) The statement “R is sequential” is equivalent to eac...