New solution to the inverse regulator problem by the polynomial matrix method
Kenji Sugimoto, Yutaka Yamamoto · International Journal of Control · 1987
This paper gives a new criterion for the inverse regulator problem in terms of polynomial matrix fractions. The generalized Kalman equation in polynomial matrix form leads to a necessary and sufficient condition for a stable feedback law to be optimal for some (unknown) quadratic performance index. This criterion consists of (i) a symmetric factorizability of a polynomial matrix, and (ii) a polynomial-type criterion that guarantees detectability. The relationship between the Riccati and Kalman equations is also established. Finally, an example is given to illustrate the new result in contrast with the existing result.