Positive Normalization of Discrete Descriptor System under Disturbance

Abstract

It is well known the descriptor systems have a wide application field. Usually it appear as a mathematical model of a real problem, mainly the model that involves the input output relationship. It is well known that a descriptor linear system has an unique solution if the pencil matrix of the system is regular. However, there are some systems that are not regular. Moreover, even though the system is regular the solution can contain the noncausal behavior. Therefore, it is necessary to normalize the descriptor system so as it has well behavior. In this paper, we propose a feedback to normalize a discrete descriptor system under disturbance. Furthermore, we establish a sufficient condition in order for the discrete descriptor system under disturbance can be normalized positively.