The main aim of this paper intends to discuss the solution of fuzzy Sylvester Matrix equation AX+XB=C where A= (aij)ÎRn´n, B= (bij) ÎRm´m are crisp M- matrices, C= (cij) ÎRn´m is fuzzy Matrix and XÎRn´m is unknown, by applying a special algorithm based on a class of ABS algorithms called Huang algorithm. At first, we transform this system to an (mn)´(mn) fuzzy system of linear equations. Then, we convert this system to three (mn)´(mn) crisp linear systems of equations, and we solve them simultaneously by ABS algorithm.

Solutions of two problems related to the Matrix equation of Sylvester type is given. In the first problem, the procedures for linear Matrix inequalities are used to con-struct the solution of this equation. In the second problem, when a Matrix is given which is not a solution of this equation, it is required to find such solution of the original equation, which most accurately approximates the given Matrix. For this, an algorithm for constructing a general solution of the Sylvester Matrix equation is used. The effectiveness of the proposed approaches is illustrated on the examples.

in this paper, differential equation of sensitivity Matrix of required velocity with respect to position vector is derived for a linearized problem of a spacecraft motion with final velocity constraint. This Matrix can be utilized for an implicit guidance of a spacecraft with final position and velocity constraint. The solution is obtained in the presence of aerodynamical force. Therefore, the resulting equation can be used for trajectory optimization. Moreover, a change of variable is presented to reduce onboard computational burden, in addition, the method is more appropriate for analytical approaches than conventional implicit equations.