On the existence of Equivalent-Input-Disturbance and multiple integral augmentation via H-Infinity Synthesis for unmatched systems

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. © 2022 ISA