We consider the problem of robust stability for uncertain systems described in terms of multiple scalar structured time-invariant perturbations, which are norm bounded. The issue we address is the role that the type of perturbation norm plays in the robust stability conditions. To this end, the L p-induced norms (for 1 p 1) on the perturbations are considered, and some simple relations between ...

We consider two spacelike separated Dirac particles and construct five invariants under the spinor representations of local proper orthochronous Lorentz groups. All constructed are identically zero for product states. The behaviour unitary evolutions that act unitarily on any subspace with fixed particle momenta is studied. have invariant absolute values such subspaces if generated by zero-mass...

We study the local asymptotics at edge for particle systems arising from: (i) eigenvalues of sums unitarily invariant random Hermitian matrices and (ii) signatures corresponding to decompositions tensor products representations unitary group. Our method treats these two models in parallel, is based on new formulas observables described terms a special family lifts, which we call supersymmetric ...

Abstract We study a quantum analogue of the 2-Wasserstein distance as measure proximity on set ? N density matrices dimension N . show that such (semi-)distances do not induce Riemannian metrics tangent bundle ...

The multiplicative perturbation bounds for weighted unitary polar factor are considered in the weighted unitary invariant norm, weighted spectral norm, and weighted Frobenius norm in this paper. As the special cases, new bounds for subunitary and unitary polar factor are also derived. These new bounds improve the corresponding results published recently to some extent. Mathematics subject class...

this paper presents h∞ control problem for input-delayed systems. a neutral system approach is considered to the design of pd controller for input delay systems in presence of uncertain time-invariant delay. using this approach, the resulting closed-loop system turns into a specific time-delay system of neutral type. the significant specification of this neutral system is that its delayed coeff...

The free convolution ⊞ is the binary operation on the set of probability measures on the real line which allows to deduce, from the individual spectral distributions, the spectral distribution of a sum of independent unitarily invariant square random matrices or of a sum of free operators in a non commutative probability space. In the same way, the rectangular free convolution ⊞ λ allows to ded...

In this paper, we consider an electron moving on a 2D noncommutative plane immersed in constant magnetic field under the influence of polynomial potential. We obtain gauge invariant energy spectra system using 2-parameter family unitarily equivalent irreducible representations nilpotent Lie group GNC that were worked out detail Chowdhury (2017). work cases anisotropic harmonic potential and Hal...

Let A be a unital separable C∗-algebra and B = C ⊗ K, where C is a unital C∗-algebra. Let τ : A → M(B)/B be a weakly unital full essential extensions of A by B. We show that there is a bijection between a quotient group of K0(B) onto the set of strong unitary equivalence classes of weakly unital full essential extensions σ such that [σ] = [τ ] in KK(A,B). Consequently, when this group is zero, ...