Numerical solution of Sylvester matrix equations: Application to dynamical systems

Abstract

Many problems of control theory specially dynamical system lead to Sylvester equations. In this paper, we employ an iterative method of optimization based on partial swarm theory to solve the Sylvester system. To this purpose we consider dynamical system with different construction of state observer which lead to Sylvester observer equation. Using Pso to optimize the solution, obtain the solution with high accuracy comparison with other numerical methods, since the stability analysis of particle dynamics of PSO associated with the best particle is based on nonlinear feedback systems. Finally, some examples demonstrate the efficiency of the proposed method.