"An improved eigenvalue sensitivity is presented for digital controller realisations via the
orthogonal Hermitian transform, subject to ﬁnite word length (FWL) effects. This approach can
preserve the stability of the closed-loop system when the designed stabilising digital controllers are
actually implemented with FWL by using the mode of ﬁxed-point arithmetic. A performance index
deﬁned by eigenvalue sensitivity of the closed-loop system is evaluated by the mixed matrix-2/
Frobenius norms, so that the eigenvalues of the closed-loop system, from inﬁnite precision after
using an FWL implemented digital controller, become limited precision, the inﬂuence suffered is
minimal. Then, the optimal similarity transformation for the controller is obtained via the
orthogonal Hermitian transform. Thus, a minimum bit number used for implementing the
stabilising digital controllers can be obtained from the performance index and the optimal similarity
transformation under certain stability criteria. The main contributions are that this approach
provides an analytical closed-form solution for the optimal transformation and leads to the
implementation of the stabilising controllers with a lower bit number when using this optimal one.
Finally, a numerical example is used to illustrate the effectiveness of the proposed scheme."