New equations for the time-dependent regulator problem

This correspondence presents a derivation of an alternate set of equations for determination of the optimal feedback gain matrix for the time-dependent linear regulator problem. In contrast to the usual Riccati equation approach, the new system is composed of only equations, where is the number of systems input terminals. As payment for this reduction in number of equations, however, the new system is not entirely general, being restricted to constant control matrices , with arbitrary dynamics and cost matrices and , respectively.