This paper is on a discrete controller order reduction with the closed-loop stability and performance guaranteed. to achieve this, after finding the solutionsof two lyapunov inequalities and balancing the full order controller system, we find the reudced order controlers using the balanced truncation (BT) and the balanced singular perturbation approximation (BSPA). When the solutions of the two lyapunov inequalities exist, it is shown that the resulting controllers guarantee the closed-loop stability, and .inf.-norm error bounds are derived for the closed-loop performance region for the BT and in low frequency region for the BSPA. Finally, a numerical example is given to illustrate the validity of the proposed method.
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