State space realization of bilinear continuous-time input-output equations

• Published in: International journal of control Vol. 80; no. 10; pp. 1607 - 1615
• Main Authors: Kotta, Ü., Mullari, T., Zinober, A. S. I., Kotta, P.
• Format: Journal Article
• Language: English
• Published: London Taylor & Francis Group 01-10-2007; Taylor & Francis
• Subjects: Applied sciences; Computer science; control theory; systems; Control theory. Systems; Exact sciences and technology; Bilinear system; Equations of state; Differential equation; Discrete time; Continuous time; State space method; Modeling
• ISSN: 0020-7179; 1366-5820
• DOI: 10.1080/00207170701447106

This paper studies the realizability property of continuous-time bilinear input-output (i/o) equations in the classical state space form. Constraints on the parameters of the bilinear i/o model are suggested that lead to realizable models. The paper proves that the 2nd order bilinear i/o differential equation, unlike the discrete-time case, is always realizable in the classical state space form. The complete list of 3rd and 4th order realizable i/o bilinear models is given and two subclasses of realizable i/o bilinear systems are suggested. Our conditions rely basically upon the property that certain combinations of coefficients of the i/o equations are zero or not zero. We provide explicit state equations for all realizable 2nd and 3rd order bilinear i/o equations, and for one realizable subclass of bilinear i/o equations of arbitrary order.