Synthesis of Minimum Statistical Sensitivity Structures with Fewer Parameters in State--Space Systems.

In state-space systems, since the minimum statistical sensitivity structures obtained by the equivalent transformations are generally completely dense, they have defects and the numbers of parameters are very large. If this point can be improved, realizations with lower sensitivity and fewer parameters are obtained. This paper presents a synthesis of new minimum statistical sensitivity structures with fewer parameters as one such realization. First, to compare sensitivities of various realizations, assuming that only noninteger elements in the coefficient matrices contain small variations, the statistical sensitivity is defined. Since the sensitivity is invariant under the orthogonal transformations, using the symmetry of the coefficient matrices of the balanced realizations which are the members of the minimum statistical sensitivity structures, it is shown that a minimum statistical sensitivity structure can be realized with fewer parameters by defining an appropriate orthogonal transformation matrix. The number of parameters required in the proposed structure depends on the pole-zero configuration of the transfer function. Finally, various realizations are compared using numerical examples. As the parameters decrease, the insensitive elements increase. Therefore, the realization proposed in this paper has the lowest sensitivity. [ABSTRACT FROM AUTHOR]