Structural state space sensitivity in linear systems (Q1084361)

The concept of input balanced realization of a given matrix transfer function is applied here to find the particular minimal state space realization that minimizes the output noise gain subject to a \(\ell_ 2\)-scaling constraint. The sensitivity measure is new in the respect that it is defined by means of transformation independent noise. In practical terms this corresponds to e.g. roundoff noise in digital filtering. The optimum solution, known in the case of no structural constraints, is here derived by means of an initial balanced realization. Furthermore, the optimum is found under some structural constraints: a state covariance decoupling and a q-markov matching structure.