Two formulations of exponentially weighted enhanced LQ controllers

Properties of a class of multi-input multi-output digital controllers are examined. The controllers incorporate three features: (1) optimal gains associated with known exogenous inputs; (2) penalties imposed both on squares of first backward differences in control actions and on control actions squared: and (3) exponential weighting to insure bounds on closed-loop eigenvalues. Two versions of exponential weighting are treated. Results are given both for the finite-horizon versions of the problems and for the infinite-horizon versions of the problems. The results include expressions for optimal feedback gains and for optimal preview gains. For the infinite-horizon versions of the problems, relationships are derived between the optimal closed-loop eigenvalues and the eigenvalues associated with the preview gains. Two examples are given to illustrate properties of these conditions