The structure character of system transfer matrices can be used to solve a class of singular ��H��∞ control problem and a reduced order ��H��∞ controller can be constructed in explicit form either by linear matrix inequations method or two algebra Riccati equation method. The order of the system ��H��∞ controller can further be reduced by use of system unstable invariant zeros. Based on two algebra Riccati equation method especially the structure of the system Hamilton matrix and system observability theory, the role of invariant zeros in constructing system reduced order controllers was given. That is, by the suitable selection of free parameters of the system ��H��∞ controller, some points which were symmetry with the unstable invariant zeros about the imaginary axis became the stable poles of the system controller which were not observable and could be reduced from the system, thus could get further reduced order controller.
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