A Feedback Compensation Scheme for the Linear Quadratic Regulator with Zero End-Point

Abstract

This paper focuses on the implementation of a state-feedback compensator for the solution of the linear quadratic control problem with an arbitrary initial state and with null end-point for discrete-time systems. The regulator, which ensures internal stability of the closed-loop system, is linear time-invariant, and is herein described in its inner structure. The solution of the optimization problem is based on a finite horizon parametrization of the solutions of the associated extended symplectic difference equation.