In this paper, the existence of a solution for the transformation of the disturbances from the unmatched cases to the matched one is investigated. The usage of matched/unmatched disturbance notions and the underlying assumptions are clarified. Then, a simplified definition is introduced to obtain a set of performance metrics to be used in observer design. Using bilinear pole shifting and multiple integral augmentation to the plant, not only the stabilizability/detectability conditions but also infinity-norm bounds for unstable MIMO systems are derived. Then, the solvability of the augmented Hamiltonian matrices to get stabilizing solutions via standard H∞-Synthesis is explained. Finally, the solutions, definitions, and assumptions are validated through numerical examples.
Keywords: -Synthesis; Hamiltonian matrices; MIMO disturbance observer; Matched/Unmatched disturbances; Multiple integral augmentation.
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