A Robustness Analysis of Controllers Quadratically Stabilizing Linear Discrete-Time Systems Under Bounded Input Disturbances

Abstract

This paper presents a parameterization and robustness analysis of state-feedback controllers that quadratically stabilize a linear discrete-time system with single control input corrupted by amplitude bounded disturbances. Stabilizing controllers are parameterized by a positive definite matrix corresponding to the state weight matrix in cheap control. This parameter determines the region where the state is constrained to lie in a time-average sense. This region is inscribed in the boundary of an invariant set, where the state is always constrained to lie. Also the state can escape from anywhere in a scaled invariant set, which is inscribed in the boundary of this region. These observations enable to reveal the state components robust or sensitive to the input disturbances.