Abstract
AbstractNecessary and sufficient conditions for the existence of a minimizing discrete‐time ℋ︁2 control, when assumptions are the internal stabilizability and left‐ and right‐invertibility of transfer matrices G12 and G21, are presented. Unlike the existing approach with a transformation into a disturbance decoupling problem with a measurement feedback and internal stability, we use a direct approach: from frequency to time domain. The first main result gives a necessary and sufficient existence condition for ℋ︁2 control: that a minimal realization of the infimal controller is stabilizing. The second main result presents a realization of an optimal controller that has a state observer form, identical to the form of the regular case, except that the state‐feedback gain matrix and the observer gain matrix are replaced by some stabilizing matrices. Copyright © 2009 John Wiley & Sons, Ltd.
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