Abstract: The multidelays linear control systems described by
difference differential equations are often studied in modern control
theory. In this paper, the delay-independent stabilization algebraic
criteria and the theorem of delay-independent stabilization for linear
systems with multiple time-delays are established by using the
Lyapunov functional and the Riccati algebra matrix equation in the
matrix theory. An illustrative example and the simulation result, show
that the approach to linear systems with multiple time-delays is
effective.
Abstract: In the present paper, we propose numerical methods for solving the Stein equation AXC - X - D = 0 where the matrix A is large and sparse. Such problems appear in discrete-time control problems, filtering and image restoration. We consider the case where the matrix D is of full rank and the case where D is factored as a product of two matrices. The proposed methods are Krylov subspace methods based on the block Arnoldi algorithm. We give theoretical results and we report some numerical experiments.
Abstract: The real representation of the quaternionic matrix is
definited and studied. The relations between the positive (semi)define
quaternionic matrix and its real representation matrix are presented.
By means of the real representation, the relation between the positive
(semi)definite solutions of quaternionic matrix equations and those of
corresponding real matrix equations is established.
Abstract: We are concerned with a class of quadratic matrix
equations arising from the overdamped mass-spring system. By
exploring the structure of coefficient matrices, we propose a fast
cyclic reduction algorithm to calculate the extreme solutions of the
equation. Numerical experiments show that the proposed algorithm
outperforms the original cyclic reduction and the structure-preserving
doubling algorithm.
Abstract: In this paper, a novel wave equation for electromagnetic
waves in a medium having anisotropic permittivity has been derived
with the help of Maxwell-s curl equations. The x and y components
of the Maxwell-s equations are written with the permittivity () being
a 3 × 3 symmetric matrix. These equations are solved for Ex , Ey,
Hx, Hy in terms of Ez, Hz, and the partial derivatives. The Z
components of the Maxwell-s curl are then used to arrive to the
generalized Helmholtz equations for Ez and Hz.