A Parametrization of Controllers Robust to Input Disturbances with Bounded Amplitude

Abstract

This paper presents a parametrization of all static state-feedback controllers that stabilize a single-input linear discrete-time system in the presence of input disturbance with bounded amplitude. The controllers are required to constrain the upper bound of a quadratic form of the state using a priori knowledge of the worst-case amplitude of disturbances. All stabilizing controllers are parametrized by a positive definite matrix representing the state weight in cheap control.