2-D state-space realizations with fewer multipliers and invariant norms

A similarity transformation that introduces zero coefficients in the A matrix of a local state-space (LSS) realization is presented. The transformation is orthogonal and thus preserves
\parallel A \parallel
. This guarantees that the number of multipliers is reduced without sacrificing zero input stability to nonlinearities satisfying
|Q(x_{i})| \leq |x_{i}|
. It is shown that the transformation does not affect the sensitivity. The results are extended to the generalized asymmetric half-plane state-space model. An example of a general
1 - Q
second-order filter is given.