Discrete balanced controller order reduction

This paper is on a discrete controller order reduction with guaranteed closed loop stability and performance. To achieve this, after finding the solutions of two Lyapunov inequalities and balancing the full order controller system, we obtain the reduced order controllers using the generalized singular perturbation approximation (GSPA) at particular points of complex z-plane. When the solutions of the two Lyapunov inequalities exist, it is shown that the resulting reduced order controllers are guaranteed to stabilize the corresponding systems, and ∞-norm error bounds are derived for the closed loop performance degradation