Title: Polynomial matrix approach to the linear descriptor systems

Biography:

Wataru Kase received his BE, ME and PhD degrees from Sophia University in 1985, 1987 and 1990 respectively, and joined the Dept of Information Engineering, Nagoya University, as a research associate. In 1996, he moved to the Dept of Electrical and Electric Systems Engineering, Osaka Institute of Technology, where he is currently a professor. His research interests include linear system theory, multivariable control systems and adaptive control systems.

Abstract

The descriptor systems are convenient and natural modeling process for the practical plants. The state space method and the geometric approach are used to study the structure properties and to design the controllers. Comparing these methods, there are not so many literatures using the polynomial matrix approach. In this paper, we will propose an analysis method of the descriptor systems using the regularizing polynomial matrix. The regularizing polynomial matrix compensates the singularity of the descriptor systems, like an interactor matrix for rational function matrices. In fact, the regularizing matrix is almost equivalent to an interactor. Although some derivation methods of the interactor were proposed, almost of all were complex. Mutoh and Ortege proposed the algebraic equation, which the coefficient matrices of the interactor should be satisfied.  However, the solution method was not adequate for computer calculations. The authors proposed a solution of the equation using Moore-Penrose pseudo-inverse. Since a function to calculate the pseudo-inverse is available in some standard software for control engineering, the method is adequate for computer calculations.
We will show that the degree of the regularizing polynomial matrix presents a structural aspect of a given descriptor system. That is, there exists the regularizing matrix of degree one if a given system has no impulsive mode. There exists the regularizing matrix of degree two if a given system has some impulsive modes. We will also a condition for the impulsive controllability of the descriptor systems using the analysis. A method to stabilize the descriptor systems using the polynomial matrix approach will be given.