Asymptotically tracking in high-order descriptor linear systems

This paper considers model following control problem in high-order descriptor linear systems. The problem is converted into two high-order Sylvester matrix equations and stabilization of the high-order descriptor linear system. According to the solution of high-order eigenstructure assignment, parametric solutions to the stabilization problem are presented. Further by combining the two high-order Sylvester matrix equations into a generalized one, the parametric expressions for the feedback gain matrices are obtained. An illustrative example is given to show the effectiveness of the method.