Covariance control theory provides a parametrization of all controller
s that assign a given state covariance matrix to the closed-loop syste
m. Such controllers are not unique. In this note we obtain the analyti
c expressions for the covariance controllers that minimize the require
d control effort. These are solutions to a minimum-effort/guaranteed-p
erformance design problem, in the sense that the required control effo
rt is minimized subject to performance constraints guaranteed by a spe
cified state covariance matrix assignment. In a different interpretati
on of the results, the solutions to a minimum-effort controller redesi
gn problem are obtained. Both continuous-time and discrete-time result
s are presented. (C) 1997 Elsevier Science Ltd.