We provide necessary and sufficient conditions for the uniqueness of solution of the generalized Sylvester and ⋆-Sylvester equations, AXB − CXD = E and AXB+CX ⋆ D = E, respectively, where the matrix coefficients are allowed to be rectangular. These conditions generalize existing results for the same equations with square coefficients. Our characterization reveals unexpected constraints regardin...

This paper is concerned with the numerical solution of large scale Sylvester equations AX −XB = C, Lyapunov equations as a special case in particular included, with C having very small rank. For stable Lyapunov equations, Penzl (2000) and Li and White (2002) demonstrated that the so called Cholesky factor ADI method with decent shift parameters can be very effective. In this paper we present a ...

An iterative algorithm is constructed to solve the generalized coupled Sylvester matrix equations AXB − CYD,EXF − GYH M,N , which includes Sylvester and Lyapunov matrix equations as special cases, over generalized reflexive matrices X and Y . When the matrix equations are consistent, for any initial generalized reflexive matrix pair X1, Y1 , the generalized reflexive solutions can be obtained b...

This paper is concerned with numerical solutions of large scale Sylvester equations AX −XB = C, Lyapunov equations as a special case in particular included, with C having very small rank. For stable Lyapunov equations, Penzl (2000) and Li andWhite (2002) demonstrated that the so called Cholesky factored ADI method with decent shift parameters can be very effective. In this paper we present a ge...

in this paper, we propose the least-squares method for computing the positive solution of a m  n fully fuzzy linear system (ffls) of equations, where m > n, based on kaman's arithmetic operations on fuzzy numbers that introduced in [18]. first, we consider all elements of coecient matrix are non-negative or non-positive. also, we obtain 1-cut of the fuzzy number vector solution of the n...

the aim of this paper is to show how some measures of noncompactness in the banach space of continuous functions defined on two variables can be applied to the solvability of a general system of functional integral equations . the results obtained generalize and extend several equations . an illustrative example is also presented .

in this study, the roll, yaw and depth fuzzy control of an au- tonomous underwater vehicle (auv) are addressed. yaw and roll angles are regulated only using their errors and rates, but due to the complexity of depth dynamic channel, additional pitch rate quantity is used to improve the depth loop performance. the discussed auv has four aps at the rear of the vehicle as actuators. two rule bases...