Abstract
This paper proposes a newly defined sensitivity called statistical sensitivity in continuous time state-space linear systems. The statistical sensitivity is given by using a virtual stochastic system of which coefficients and input signal are white processes. The necessary and sufficient condition for the mean square asymptotical stability is given by analyzing the convergence of the statistical sensitivity. This condition determines the upper bound of variance of coefficient variations that guarantees the stability of the system. If the coefficient variations are very small, the approximated statisitical sensitivity is represented by the controllability and observability Gramians. The approximated statistical sensitivity can be minimized under an assumption that the all elements of coefficient matrices vary. The minimum sensitivity structures are equal to balanced realizations in the wide sense. To show the validity of statistical sensitivity, the various sensitivities of three structures are compared using a numerical example. The numerical example shows that a balanced realization has much lower sensitivity than a controllablity canonical realization and a parallel realization. Furthermore, the balanced realization allows the large variance of coefficient variations that guarantees the stability.
