Low-Order Realization For Roesser Model Of Multidimensional Singular Systems Based On Matrix Transformations

Singular system is a hot research field in modern control theory.Compared with the traditional regular systems,singular systems can describe a wider range of system-s and richer connotations,also related research is more challenging.The problem of state-space model realization is a basic problem in the study of multidimensional sin-gular systems.Only after the model realization of singular systems is obtained,system analysis and design be carried out.Especially the order of model realization greatly affects the complexity of system calculation and the difficulty of simulation design.However,so far,there is still no sufficient and necessary condition to judge whether a model realization of a multidimensional singular system is minimal,so the low-order model realization problem of the multidimensional singular system urgently needs to be studied.This paper first proposes a realization method based on matrix transformations for the right matrix fraction description form of the transfer function of multidimensional singular Roesser models,which transforms the realization problem into the problem of how to obtain the objective matrix through matrix transformations.The corresponding realization steps and two techniques needed in the realization process,namely column technique and row technique,are also given.Because the transfer function of multi-dimensional singular Roesser models does not have the duality,in order to solve this problem,this paper introduces the concept of separated standard form,and thus obtains the left matrix fraction description form,the corresponding realization method is given.This allows the left and right matrix fraction descriptions of multidimensional singu-lar Roesser models to be processed in the same theoretical framework,which makes a contribute to the further exploration of the structural properties of singular systems.Due to the complexity of the structure of multidimensional singular Roesser mod-els,the order of the model obtained by the existing realization methods is still high.To solve this problem,this paper proposes a low-order model realization method based on transformation matrix construction.This method can further reduce the order of singular Roesser models to obtain a lower order model.The corresponding low-order realization procedure of the proposed method are given,and the specific details and effectiveness of the proposed method are shown through calculation and analysis of examples.Finally,this paper briefly introduces the gyro flywheel system in the spacecraft,and then the proposed realization method is applied to this system.The corresponding results show that the model order obtained by the new method is lower than the existing realization methods.This verifies the superiority of the new method in practical system application,and provides effective support for subsequent design and analysis.