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An Improved Algorithm for Computing Transfer Function Matrices of Descriptor Systems
Akitoshi Mutsuro,Masanobu Koga 제어로봇시스템학회 2016 제어로봇시스템학회 국제학술대회 논문집 Vol.2016 No.10
In this paper, we propose a numerically reliable algorithm for computing the transfer function matrix of a descriptor system. Descriptor system has widely been used. The system often arises when modelling a linear system. Linear systems such as inversion are often represented in terms of descriptor systems. Although the representation is useful, it is not appropriate for simulation and experiment. A remedy for the problem is transforming proper descriptor system into state space system by way of transfer function matrix. Numerical algorithm for computing the transfer function matrix of a descriptor system has been reported. The algorithm makes use of QZ decomposition which can be used for computing generalized eigenvalues of a matrix pencil. However, when matrices have the repeated eigenvalues, numerical errors can be generated by using the method. Furthermore, since the theory of the algorithm is based on power method which needs iterative computation, the convergence time would be slower at that time. We propose an algorithm that avoids solving generalized eigenvalue problem. Since our algorithm avoids QZ decomposition, the repeated eigenvalues does not matter. Moreover, the computational time can be estimated.