Exploiting Input Redundancy for High‐Performance Discrete‐Time LQR Control

Abstract

This paper investigates the linear quadratic regulator (LQR) problem for discrete‐time linear systems with redundant inputs. Under stabilizability and detectability assumptions, two monotonically decreasing sequences of upper bounds are derived for the stabilizing positive semidefinite solution of the discrete‐time algebraic Riccati equation. The first sequence gives explicit upper bounds, while the second further uses the Riccati equation structure and converges to the stabilizing positive semidefinite solution. These theoretical results are then applied to systems with redundant inputs, and sufficient conditions are established under which the norm of the feedback gain matrix is reduced. The proposed results extend related results in the literature. Numerical simulations are presented to support the theoretical analysis and to illustrate the effect of redundant inputs on control performance under the prescribed actuator constraints.