An efficient approach for enclosing the solution set of the interval coupled Sylvester matrix equations

In this paper, we investigate the interval coupled Sylvester matrix equations which include the well-known (generalized) Sylvester and Lyapunov matrix equations in both real and interval forms. Assuming that certain matrices are simultaneously diagonalizable, we present a fast and efficient approach for enclosing the solution set of the interval coupled Sylvester matrix equations. Our approach, which is a modification of the Krawczyk operator, enables us to reduce the computational complexity considerably. Some numerical tests are given to illustrate the effectiveness of the proposed approach.

Automated summary

In this paper, the interval coupled Sylvester matrix equations, including the (generalized) Sylvester and Lyapunov matrix equations in both real and interval forms, are investigated. A fast and efficient approach for enclosing the solution set of the interval coupled Sylvester matrix equations is presented, assuming certain matrices are simultaneously diagonalizable. The proposed approach, a modification of the Krawczyk operator, significantly reduces computational complexity. Numerical tests are provided to demonstrate the effectiveness of the approach.