An Integration-Implemented Newton-Raphson Iterated Algorithm With Noise Suppression for Finding the Solution of Dynamic Sylvester Equation

Abstract

Solving dynamic Sylvester matrix equations is a prevalent research topic and many methods have been arisen to solve the dynamic Sylvester equation, but few of them consider the noise effect. To investigate the new approach which can suppress the noise effect, integration feedback is added in the conventional Newton-Raphson iterated (CNRI) algorithm to form the proposed integration-implemented Newton-Raphson iterated (IINRI) algorithm based on the control theorem. Besides, this paper transforms the dynamic Sylvester equation into a linear equation which turns into the zeroing finding problem in further by constructing the error function. According to the theoretical analyses and the simulation results, the IINRI algorithm has higher accuracy and strong robustness under different noises (e.g. the constant noise, the linear noise, and the bounded random noise) while the performance of the CNRI algorithm is seriously degraded by the noises, which reveals that the IINRI algorithm is an efficient and powerful approach to solve dynamic Sylvester equation under noise perturbations.

Keywords

• Dynamic Sylvester equation
• integration-implemented
• Newton-Raphson iterated algorithm
• noise suppression