Frequency-domain synthesis of optimal inputs for multiinput-multioutput (MIMO) systems with process noise

This paper generalized the approach of Ref. [1] for the design of optimal inputs to MIMO systems with process or driving noise. First an expression for the information matrix is derived and it is shown to consist of two parts, one depending on the designed input and the other depending on the process noise input. The equivalence relationships between D-optimal designs and min-max designs are obtained leading up to numerical algorithms for computing globally optimal designs. Easily computable bounds are derived for the loss in performance due to suboptimal designs. It is shown that the optimal input may be chosen to have a discrete spectrum with a finite number of frequencies.