This paper is concerned with the investigation of the closed-loop structure of a discrete–time H∞ control system. It is shown that discrete–time H∞ controller is represented, like Linear Quadratic Gaussian control, as a pseudo state feedback, that is, a state feedback interconnected with an observer. However, in the discrete-time H∞ control problem the control structure is more complicated sinc...

We develop a very general operator-valued functional calculus for operators with an H∞−calculus.We then apply this to the joint functional calculus of two sectorial operators when one has an H∞calculus. Using this we prove theorem of Dore-Venni type on sums of sectorial operators and apply our results to the problem of Lp−maximal regularity. Our main assumption is the R-boundedness of certain s...

A sequence ${T_n}_{n=1}^{infty}$ of bounded linear  operators on a separable infinite dimensional Hilbert space $mathcal{H}$ is called subspace-diskcyclic with respect to the closed subspace $Msubseteq mathcal{H},$ if there exists a vector $xin mathcal{H}$ such that the disk-scaled orbit ${alpha T_n x: nin mathbb{N}, alpha inmathbb{C}, | alpha | leq 1}cap M$ is dense in $M$. The goal of t...

We construct some non-essential H-closed epireflections of W, the category of archimedean l-groups with weak order unit, that are not comparable with any known H-closed epireflections of W other than the divisible hull and the epicompletion. In preparation, we show that the free objects in any Hclosed epireflective subcategory of W must be closed under composition (see section 2 for a precise d...

The final step in the enzymatic synthesis of the ABO(H) blood group A and B antigens is catalyzed by two closely related glycosyltransferases, an alpha-(1-->3)-N-acetylgalactosaminyltransferase (GTA) and an alpha-(1-->3)-galactosyltransferase (GTB). Of their 354 amino acid residues, GTA and GTB differ by only four "critical" residues. High resolution structures for GTB and the GTA/GTB chimeric ...

Abstract: This paper presents a new algorithm for the closed-loop H∞ composite control of weakly coupled bilinear systems with time-varying parameter uncertainties and exogenous disturbance using the successive Galerkin approximation (SGA). By using weak coupling theory, the robust H∞ control can be obtained from two reduced-order robust H∞ control problems in parallel. The H∞ control theory gu...

This document contains the proofs to the theorems of the original paper. Some lemmas are also introduced. Theorem 1. Let qδ ∈ LT S(LI , LU ∪ {δ}) be a valid suspension automaton. Then, there exists a labelled transition system q ∈ LT S(LI , LU ) such that Straces(q) = traces(qδ). Proof. Follows directly from Theorem 2 in [18]. u t Algorithm 1 Construct Hypothesis H Input: A closed and consisten...

In this paper we propose some new solutions to the full information mixed H 2 =H 1 state feedback problem: the H 2 norm of the closed-loop system is minimized over a class of linearly combined state feedback laws that satisfy the speciied H 1 bound. Such mixed linearly combined controllers yield smaller closed-loop H 2 norms than those obtained by using the central solutions of the H 1 problem....

Up-to-date cosmological data analyses have shown that \textit{(a)} a closed universe is preferred by the Planck at more than $99\%$ CL, and \textit{(b)} interacting scenarios offer very compelling solution to Hubble constant tension. In light of these two recent appealing scenarios, we consider here an dark matter-dark energy model with non-zero spatial curvature component freely varying equati...