Computational Techniques Based on the Block-Diagonal Form for Solving Large Systems Modeling Problems

The reduction of the state-matrix of a linear time-invariant state-space model to a block-diagonal form by using a state coordinate transformation is equivalent with an additive decomposition of the corresponding transfer-function matrix. Computationally involved and large storage demanding algorithms for solving several systems modeling problems can be conveniently reformulated such that they perform exclusively on the low order subsystems corresponding to the individual terms of suitable additive decompositions. Important reductions of both the computational effort and required memory usually by using the reformulated algorithms and thus, their applicability can be extended to handle higher order systems. The paper presents several algorithms suitable to perform efficiently on additively decomposed systems. The effectiveness of these algorithms for solving large order systems modeling problems relies on a reliable numerical algorithm to compute the block-diagonal form of a matrix.