抄録
Descriptor systems is a generalization of the state-space model, and is a mixture of dynamic and static (nondynamic) parts. Of particular interest are the static parts. There are two types of static parts; the one is a part associated with the dynamical behavior. The other is a purely static part and it cause an ambiguity of the concepts on the structure of descriptor system. For example, we have two kinds of definitions of controllability and observability. One method of removing this ambiguity is to eliminate the purely static part and to get a minimal representation. Several reserchers have tackled this problem, but the traditional methods depend on Kronecker decomposition and are not necessarily suitable for the control system design, since Kronecker decomposition include numerically unstatble algorithms.
In this paper, we propose a new and numerically oriented algorithm to eliminate the purely static parts. At first, an eliminating procedure based on restricted system equivalence is introduced, and some features are clarified. Secondly the static parts are newly characterized in a geometric way, and the property in the aspect of solvability, controllability, and observability are discussed. Finally a numerically oriented algorithm is presented by using singular value decomposition, and the effectiveness is demonstrated in the problem of inverse system of descriptor form.
The proposed method in this paper is simple and numerically statble, so it is effective in application of control system design and analysis.
