Output frequency response function of nonlinear Volterra systems

• Published in: Automatica (Oxford) Vol. 43; no. 5; pp. 805 - 816
• Main Authors: Lang, Z.Q., Billings, S.A., Yue, R., Li, J.
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01.05.2007; Elsevier
• Subjects: Applied sciences; Computer science; control theory; systems; Control theory. Systems; Differential equation model; Exact sciences and technology; Nonlinear systems; Output frequency response; Volterra series theory; Volterra series theory; Output frequency response; Differential equation model; Nonlinear systems; Differential equation; Differential form; Non linear control; Polynomial equation; Frequency domain method; Output signal; Modeling; Volterra series; Frequency response; Volterra equation
• ISSN: 0005-1098; 1873-2836
• DOI: 10.1016/j.automatica.2006.11.013

An expression for the output frequency response function (OFRF), which defines the explicit analytical relationship between the output spectrum and the system parameters, is derived for nonlinear systems which can be described by a polynomial form differential equation model. An effective algorithm is developed to determine the OFRF directly from system simulation or experimental data. Simulation studies demonstrate the significance of the OFRF concept, and verify the effectiveness of the algorithm which evaluates the OFRF numerically. These new results provide an important basis for the analytical study and design of a wide class of nonlinear systems in the frequency domain.