In this paper, we present a method for system stabilisation through independent designs of the decentralised controller. The proposed method extends the practical applicability of the conventional μ interaction measure (μ-IM) to unstable systems. The decentralised controller is designed based on a block diagonal approximation that is different from the block diagonal elements, but has the same ...

A matrix-valued measure Θ reduces to measures of smaller size if there exists a constant invertible matrix M such that MΘM∗ is block diagonal. Equivalently, the real vector space A of all matrices T such that TΘ(X) = Θ(X)T ∗ for any Borel set X is nontrivial. If the subspace Ah of self-adjoints elements in the commutant algebra A of Θ is nontrivial, then Θ is reducible via a unitary matrix. In ...

In this paper, necessary and sufficient conditions are given for the k-regularity of block fuzzy matrices in terms of the schur complements of its k-regular diagonal blocks. A formula for k-g-inverse of a block fuzzy matrix is established. A set of conditions for a block matrix to be expressed as the sum of k-regular block matrices is obtained. Mathematics Subject Classification: 15B15; 15A09

In this report, we discuss block preconditioners used to solve the incompressible Navier-Stokes equations. We emphasize on the approximation of the Schur complement used in SIMPLE-type preconditioners. In the usual formulation, the Schur complement uses scaling with the diagonal of the convection diffusion matrix. A variant of SIMPLE, SIMPLER is studied. Convergence of the SIMPLER preconditione...

A discrete-time population model in which individuals are distributed over a discrete phenotypic trait-space is studied. It is shown that, for an irreducible mutation matrix , if mutation is small, then an interior equilibrium exists, that is globally asymptotically stable in , while for arbitrary large mutation each trait persists uniformly. For the model reduced to only two traits, conditions...

This report is devoted to the proof of the global convergence and asymptotic quadratic convergence of the serial and parallel two-sided block-Jacobi SVD algorithm. In the serial case, one pair of the off-diagonal blocks with the largest weight given as the sum of squares of Frobenius norms is annihilated. In the parallel case, using the greedy implementation of dynamic ordering and having p pro...

The operator associated to the angular part of the Dirac equation in the KerrNewman background metric is a block operator matrix with bounded diagonal and unbounded off-diagonal entries. The aim of this paper is to establish a variational principle for block operator matrices of this type and to derive thereof upper and lower bounds for the angular operator mentioned above. In the last section,...

There is normally a simple choice made in the form of the covariance matrix to be used with HMMs. Either a diagonal covariance matrix is used, with the underlying assumption that elements of the feature vector are independent, or a full or block-diagonal matrix is used, where all or some of the correlations are explicitly modelled. Unfortunately when using full or block-diagonal covariance matr...

In the class of systems with linear precoder and zeroforcing (ZF) DFE for zero-padded MIMO frequency selective channels, existing optimal transceiver designs present two major drawbacks. First, the optimal system requires a large number of bits to encode the full precoding matrix. Second, the full precoding matrix leads to complex computations. These disadvantages become more severe as bandwidt...