Abstract
Infinite-horizon linear quadratic control is re-examined and generalized to include a class of non-stationary disturbances. This revision is achieved by defining a generalized infinite-horizon linear quadratic control problem using a flexible functional analytic signal description. Specifically, an instantaneous linear quadratic output feedback problem is considered in this way. It is shown that the solution to the generalized linear quadratic problem is equivalent to the solution of the corresponding standard linear quadratic problem with disturbance and noise covariance matrices having in the generalized problem a different, more general, meaning than in the standard problem. In the generalized problem these covariance matrices are majorizing matrices that have a precise meaning even in the non-stationary signal case. This result justifies in a nice way the wide practice of interpreting the disturbance and noise covariance matrices in linear quadratic control as design variables.
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