Weighting Functions for Time-Varying Feedback Systems

The weighting functions for a linear time-varying system provide a means for determining system response to an arbitrary input, and also the mean square output with white noise input. The weighting functions as obtained by direct simulation are not in convenient form for such computation, but can be obtained in such form by use of the adjoint of the original system. A method is presented for the synthesis of the adjoint system for a given linear time-varying feedback system. The method is based on a physical argument in which outputs due to two inputs which place identical initial conditions in the system are equated.