The classical Cayley-Hamilton theorem (Gantmacher, 1974; Kaczorek, 1988; Lancaster, 1969) says that every square matrix satisfies its own characteristic equation. Let A ∈ Cn×n (the set of n × n complex matrices) and p(s) = det[Ins − A] = ∑n i=0 a si, (an = 1) be the characteristic polynomial of A. Then p(A) = ∑n i=0 aiA i = 0n (the n × n zero matrix). The Cayley Hamilton theorem was extended to...

A system of n linear differential equations xy'{x) =x~8B{x)y(x) is considered, in which s is a positive integer and B(x) is a formal power series. In a preceding paper [6] the author has developed a method for evaluating a formal fundamental matrix solution to the system. This method leads to the algebraic treatment of certain singular matrix pencils. In the present paper the author provides so...

Solving large scale system of Simultaneous Linear Equations (SLE) has been (and continue to be) a major challenging problem for many real-world engineering and science applications. Solving SLE with singular coefficient matrices arises from various engineering and sciences applications [1]-[6]. In this paper, efficient numerical procedures for finding the generalized (or pseudo) inverse of a ge...

1.1 Classes of systems to be considered It should be noticed that in some systems we must consider their character of dynamic and static state at the same time. Singular systems (also referred to as degenerate, descriptor, generalized, differential-algebraic systems or semi-state) are those, the dynamics of which are governed by a mixture of algebraic and differential (difference) equations. Re...

This paper discusses a generalized quadratic stabilization problem for a class of discrete-time singular systems with time-delay and nonlinear perturbation (DSSDP), which the satisfies Lipschitz condition. By means of the S-procedure approach, necessary and sufficient conditions are presented via a matrix inequality such that the control system is generalized quadratically stabilizable. An expl...

In this paper, we present a computational method for solving boundary integral equations with loga-rithmic singular kernels which occur as reformulations of a boundary value problem for the Laplacian equation. Themethod is based on the use of the Galerkin method with CAS wavelets constructed on the unit interval as basis.This approach utilizes the non-uniform Gauss-Legendre quadrature rule for ...