Linear quadratic regulators with eigenvalue placement in a specified region

A linear optimal quadratic regulator is developed for optimally placing the closed-loop poles of multivariable continuous-time systems within the common region of an open sector, bounded by lines inclined at ±π/2k (k = 2 or 3) from the negative real axis with a sector angle ≤π/2, and the left-hand side of a line parallel to the imaginary axis in the complex s-plane. Also, a shifted sector method is presented to optimally place the closed-loop poles of a system in any general sector having a sector angle between π/2 and π. The optimal pole placement is achieved without explicitly utilizing the eigenvalues of the open-loop system. The design method is mainly based on the solution of a linear matrix Lyapunov equation and the resultant closed-loop system with its eigenvalues in the desired region is optimal with respect to a quadratic performance index.