Discrete-time linear system order-reduction via balancing transformation using the method of singular perturbations

Order-reduction techniques based on system balancing are developed for linear discrete systems using the method of singular perturbations. The generalized residualization technique is introduced with three variants as improved tools for order-reduction at low and medium frequencies. The newly introduced techniques have the same theoretical upper error bound with respect to the H,, norm of the reduced-order system as the existing techniques, but simulation results show the superiority of the new techniques at low and medium frequencies. New techniques are proposed to perform order-reduction of highly oscillatory lightly damped linear discrete-time systems by employing the method of singular perturbations and balancing transformation. For systems with highly oscillatory lightly damped modes the obtained reduced-order system is based on the fast subsystem.