A design method of controllers which ensure internal stability and attain asymptotically H∞ disturbance attenuation is presented. The design procedure consists of two steps: (1) to design an H∞ state feedback control via an algebraic Riccati equation approach; and (2) under a certain minimum-phase condition, to recover the achievable performance asymptotically by applying high-gain observers. It makes use of the perfect observation for the design of high-gain observers. It is shown that the asymptotic recovery can be attained by using reduced-order observers, provided there is no direct feedthrough of controls and disturbances in observations.
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