Riccati equation solution of the minimum time output control problem

By taking a geometrical approach, and by using a type of orthogonality in constructing bases for the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</tex> th controllable subspaces, a general solution is derived for the multivariable minimum time output control problem. The solution is easier to implement than solutions derived by traditional approaches to output control, and in fact it is shown that the optimal control sequence may be constructed from the solution to a specialized Riccati equation. This new approach thus relates geometrical approaches to the problem to the previously known result that output control is just a special case of the singular linear quadratic optimal control problem.