On Classical State Space Realizability of Bilinear Input-Output Differential Equations

• Published in: 2006 14th Mediterranean Conference on Control and Automation pp. 1 - 6
• Main Authors: Kotta, U., Mullari, T., Kotta, P., Zinober, A.S.I.
• Format: Conference Proceeding
• Language: English
• Published: IEEE 01-06-2006
• Subjects: Control design; Control theory; Differential equations; Nonlinear equations; Nonlinear systems; Parameter estimation; Polynomials; State-space methods; System identification
• ISBN: 0978672011; 9780978672010
• DOI: 10.1109/MED.2006.328729

This paper studies the realizability property of continuous-time bilinear 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