An energy approach to controllability

The authors formulate an energy approach to the control of linear systems. Recent ideas developed for balancing coordinate transformations motivate this approach. Specifically, the geometry of the controllability Gramian and its relationship to the system eigenstructure underlie the controllability of a system from an input energy perspective. After detailing these ideas, the authors describe an algorithm for constructing state feedback to achieve a desired Gramian geometry in a minimum-norm sense. This provides a means of eigenstructure improvement without direct eigenstructure assignment