Based on the Hermitian and skew-Hermitian splitting (HSS) iteration technique, we establish a generalized HSS (GHSS) iteration method for solving large sparse continuous Sylvester equations with non-Hermitian and positive definite/semidefinite matrices. The GHSS method is essentially a four-parameter iteration which not only covers the standard HSS iteration but also enables us to optimize the ...

The modified Hermitian and skew-Hermitian splitting (MHSS) iteration method and preconditioned MHSS (PMHSS) iteration method were introduced respectively. In the paper, on the basis of the MHSS iteration method, we present a PMHSS iteration method for solving large sparse continuous Sylvester equations with non-Hermitian and complex symmetric positive definite/semi-definite matrices. Under suit...

It is being proposed in this paper a computational algorithm for acquiring the output feedback gain matrix in linear systems stabilization problems by regional pole placement in LMI regions. The output feedback controller is obtained through the solution of the coupled Sylvester equations. It is shown the existence of output feedback matrix providing conditions in which this problem has a solut...

We consider the problem of strong stabilization of descriptor systems via output feedback. The proposed results are based on the concept of (C, A, E, B)-invariance and its algebraic characterization by coupled Sylvester equations and coupled Lyapunov-like equations. Based either on eigenstructure assignment techniques or on the solution of linear matrix inequalities and equalities, we propose a...

the linear system of equations ax = b where a = [aij ] in cn.n is a crispsingular matrix and the right-hand side is a fuzzy vector is called a singularfuzzy linear system of equations. in this paper, solving singular fuzzy linearsystems of equations using generalized inverses such as drazin inverse andpseudo-inverse are investigated.

For a generic n-degree polynomial system which contains n+1 polynomials in n variables, we give the construction of the generic mixed Cayley-Sylvester resultant matrix. There are n− 1 generic mixed Cayley-Sylvester resultant matrices between the classical Cayley resultant matrix and the classical Sylvester resultant matrix. The entries of these new resultant matrix are of degree m(1 < m < n + 1...

Based on the higher-order restricted flows, first type of integrable deformed fourth-order matrix NLS equations, that is, equations with self-consistent sources (FMNLSSCS), is derived. By virtue $${\bar{\partial }}$$ -dressing method, second called NLS–Maxwell–Bloch system (FMNLS-MB) presented. We prove equivalence FMNLSSCS and FMNLS-MB successfully. Furthermore, N-soliton solutions are explici...