Minimum input trace for multiple input multiple output linear systems

Specification of the cross spectra for a multiple-input/multiple-output (MIMO) vibration test is challenging. This paper presents a method for tests where the specifications of the output (the control points) autospectra are available. The autospectra of the outputs are specified and cross spectra between the outputs are derived that will minimize the trace of the autospectra of the inputs (the drive signals) with the constraint that the input spectral density matrix is positive definite. The hypothesis is that nature likes a minimum energy solution.