A Gramian matrix approach to synthesizing finite-frequency H2 controller

Abstract

This paper studies the H2 control problem for linear continuous-time systems over a finite-frequency range. Using the finite-frequency Gramian matrix approach, a necessary and sufficient condition is obtained for the characterization of the finite-frequency H2 performance of a Hurwitz stability system. With such a characterization, a sufficient condition for the solvability of the finite-frequency H2 control problem is derived. An iterative algorithm is then constructed to solve the corresponding controller gain numerically. Finally, a numerical example of a two-cart-one-spring system is given to illustrate the effectiveness of the proposed scheme.