Conversion of descriptor representations to state-space form: an extension of the shuffle algorithm

This paper proposes a systematic procedure for the determination of state-space models from an available descriptor representation of a linear dynamic system. The goal is to determine a state equation, a set of algebraic equations and an output equation in terms of the state and input variables. It is shown that standard methods may fail to convert the descriptor representation to state-space form, even for simple electrical circuit models obtained from Kirchoff’s laws and constitutive element equations. A novel procedure to address this problem is then proposed as an extension of the classic shuffle algorithm combined with a singular value decomposition approach. In addition to an illustrative example involving a simple electrical circuit, the proposed method is employed in a case study involving the modeling of three-dimensional RLC networks with a large number of components.