On the Estimation of Unknown Input and Output Disturbances in Discrete-Time Linear Systems

Abstract

One of the necessary conditions for the existence of unknown input observers (UIOs) is a matrix rank condition. For the plants for which this matrix rank condition is satisfied, a number of UIO architectures were reported in the literature. In this paper, the proposed estimator architectures are for the plants for which the matrix rank condition for the existence of UIOs is not satisfied. To construct the proposed estimators, (δ + 1) observations are collected that are then used to form an augmented system that satisfies the matrix rank condition, where δ is a design parameter. The design of the unknown input and output disturbance estimators are given in terms of linear matrix inequalities (LMIs). The unknown input and output disturbance estimation errors are guaranteed to be l <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> -stable with computable performance level.