STATISTICAL SENSITIVITY AND MINIMUM SENSITIVITY STRUCTURES WITH FEWER COEFFICIENTS IN DISCRETE-TIME LINEAR-SYSTEMS

A statistical sensitivity in discrete time state-space linear systems is defined by using a virtual system of which coefficients are stochastically varied. The necessary and sufficient condition for the mean square asymptotical stability can be given by analyzing the covergence of the state covariance matrix of the virtual system. This condition determines an upper bound of variance of coefficient variations that guarantees the stochastic stability. The minimum sensitivity structures can be synthesized by giving two assumptions to simplify the sensitivity measure. The minimum sensitivity structures have much more coefficients than the other canonical structures in general. To reduce the number of coefficients, this paper synthesizes new minimum sensitivity structures, which have fewer coefficients and lower sensitivity than the usual minimum sensitivity structures. The number of coefficients depends on the pole-zero configuration of the transfer function. Two numerical examples show that the minimum sensitivity structures have much lower sensitivity than the other realizations. © 1990 IEEE