Minimal realisation of bilinear and quadratic input-output difference equations in state-space form

• Published in: International journal of control Vol. 84; no. 12; pp. 2024 - 2034
• Main Authors: Belikov, J., Kotta, P., Kotta, Ü., Zinober, A.S.I.
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis Group 01-12-2011; Taylor & Francis; Taylor & Francis Ltd
• Subjects: Algorithms; Applied sciences; bilinear and quadratic input-output difference equations; Computation; Computer science; control theory; systems; Control theory. Systems; Difference equations; discrete-time systems; Exact sciences and technology; Lists; Mathematical analysis; Mathematical models; Modelling and identification; polynomial method; state-space realisation; Studies; Vector spaces; Vectors (mathematics); discrete-time systems; Differential form; State space; State space method; Polynomial method; Difference equation; Modeling; Quadratic equation; bilinear and quadratic input―output difference equations; Equations of state; Vector space; Discrete time; state-space realisation
• ISSN: 0020-7179; 1366-5820
• DOI: 10.1080/00207179.2011.631587

This article studies the realisability property of discrete-time bilinear and quadratic input-output (i/o) equations in the classical state-space form. Constraints on the parameters of the i/o model are suggested that lead to realisable models. Using new formulae for computing basis vectors of certain vector spaces of differential one-forms, we present in this article the complete list of the third- and fourth-order realisable i/o bilinear models, and a new realisable subclass of an arbitrary order is suggested. Moreover, we provide the sufficient conditions of the second- and third-order realisable i/o quadratic models, respectively. All the developed theory and algorithms are illustrated by means of several examples.