Multiple parameter iteration-correction method for solving the generalized mixed-type Lyapunov matrix equation AX+XB+CXD=F is discussed.

In this paper,we study the problem about the symmetric positive definite solution to a class of mixed-type Lyapunov matrix equations.

Symmetric solution of the mixed-type Lyapunov matrix equation A~TX+XA+B~TXB= C is solved by using an iterative algorithm with a parameter.

Using Schur triangular theorem of complex square matice and induction,an elementary proof for the condition of existence and uniqueness of Lyapunov matrix equation is presented.

The content of this paper consists of two parts:part one is how to solve the linear systems Ax=b iteratively,which coefficient matrices are centrosymmetric matrices; part two pays attention to solving the Lyapunov matrix equations and Sylvester matrix equations in control theory by numcrical methods.

Solving linear and nonlinear matrix equations such as the Lyapunov matrix equation and the Riccati matrix equation is one of important topics in the fields of numerical algebra and nonlinear analysis.

In this paper,a necessary and sufficient condition on stability for discrete-time singular systems is given mainly by applying special restricted systems equivalent transformation and a appropriate generalized Lyapunov equation.

This paper studies the following generalized Lyapunov equation PA+A′P+∑ni=1C ′ iPC i=-Q Under the assumption of exact observability, prove that the above equation has a positive solution is equivalent to the stability of (A,∑ n i=1 C i).

Based on a complete parametric solution to a class of generalized Sylvester matrix equations,parametric expressions for all the gain matrices of the observer are derived.