Statistical sensitivity and minimum sensitivity structures with fewer coefficients in discrete time linear systems

Statistical sensitivity in discrete-time state-space linear systems is defined, using a virtual system whose coefficients are stochastically varied. The necessary and sufficient condition for the mean-square asymptotical stability is obtained by analyzing the convergence of the state covariance matrix of the virtual system. This condition determines an upper bound on the variance of coefficient variations that guarantees stochastic stability. Minimum-sensitivity structures can be synthesized by using two assumptions to simplify the sensitivity measure. The minimum-sensitivity structures have many more coefficients than the other canonical structures in general. The authors synthesize minimum-sensitivity structures that 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