State space analysis of singular systems via orthogonal series

Three novel alternative approaches for state-space analysis of singular systems via orthogonal series are presented. All three approaches yield explicit expressions for the state vector coefficient matrix involving only multiplication of matrices of small dimensions. The combination of the advantages (computational, structural, etc.) of all three approaches appears to be superior to the advantages of all known techniques for the analysis of singular systems via orthogonal series. The first two approaches make use of the differentiation operational matrix. The third approach has the advantage that it does not use any system decomposition or state transformation