Linear Quadratic Regulators with Prescribed Eigenvalues for a Family of Linear Systems

In this paper a new design procedure is proposed that combines linear quadratic optimal control (LQ) with pole assignment. In LQ-problems the quadratic weights are usually found by trial and error to get good time behavior. In contrast the proposed method modifies a given state weighting matrix such that all closed-loop poles are located in a specified region of the complex s-plane. It is shown that this can be done with the smallest possible increase of the quadratic performance index under consideration. The procedure is extended to the design of robust control systems where the plant is described by a family of linear systems according to different operational conditions. The control of a F4E aircraft demonstrates the achievements of the new procedure.