In this paper, the row by row decoupling problem by static state feedback is studied for regularizable singular square systems. The problem is handled in matrix polynomial equation setting. The necessary and sufficient conditions on decouplability are introduced and an algorithm for calculation of feedback gains is presented. A structural interpretation is also given for decoupled systems.

The estimation of the positive definite solutions to perturbed discrete Lyapunov equations is discussed. Several upper bounds of the positive definite solutions are obtained when the perturbation parameters are norm-bounded uncertain. In the derivation of the bounds, one only needs to deal with eigenvalues of matrices and linear matrix inequalities, and thus avoids solving high-order algebraic ...

We present a new method for the nonlinear approximation of the solution manifolds of parameterized nonlinear evolution problems, in particular in hyperbolic regimes with moving discontinuities. Given the action of a Lie group on the solution space, the original problem is reformulated as a partial differential algebraic equation system by decomposing the solution into a group component and a sp...

We study the matrix equation XA − AX = X p in M n (K) for 1 < p < n. It is shown that every matrix solution X is nilpotent and that the generalized eigenspaces of A are X-invariant. For A being a full Jordan block we describe how to compute all matrix solutions. Combinatorial formulas for A m X ℓ , X ℓ A m and (AX) ℓ are given. The case p = 2 is a special case of the algebraic Riccati equation.

Most problems in algebra, at some stage, must consider algebraic equations. Sometimes solving them, other times producing them – so their existence manifests a desired structure. Akin to doing differential equations, a researcher in algebraic equations must specialize to get somewhere. My speciality is algebraic equations in two variables, say w and z, where one variable, say z, interprets as a...

A simple and effective method based on Haar wavelets is proposed for the solution of Pocklington's integral equation. The properties of Haar wavelets are first given. These wavelets are utilized to reduce the solution of Pocklington's integral equation to the solution of algebraic equations. In order to save memory and computation time, we apply a threshold procedure to obtain sparse algebraic ...

It is well known that the parabolic partial differential equations in two or more space dimensions with overspecified boundary data, feature in the mathematical modeling of many phenomena. In this article, an inverse problem of determining an unknown time-dependent source term of a parabolic equation in general dimensions is considered. Employing some transformations, we change the inverse prob...

The paper deals with the associated algebraic matrix Riccati equation (AAMRE), closely related to the standard algebraic matrix Riccati equation arising in the theory of linear-quadratic optimisation and filtering. The sensitivity of the AAMRE relative to perturbations in its coefficients is studied. Both linear local (norm-wise and componentwise) and non-linear non-local perturbation bounds ar...

The objective of this paper is to study the theoretical analysis of linear differential-algebraic equations (DAEs) of higher order as well as the regularity and singularity of matrix polynomials. Some invariants and condensed forms under appropriate equivalent transformations are established for systems of linear higher-order DAEs with constant and variable coefficients. Inductively, based on c...