Identification of discrete-time bilinear systems through equivalent linear models

Abstract

This paper presents a novel method for identification of discrete-time, time-invariant state-space models of bilinear dynamical systems using the steady-state portion of a single input/multiple output time-history measurements. These measurements are recorded by exciting the system with a linear combination of sine and cosine functions of user-selected frequencies enriched by a subtle amount of random component. The proposed method relies on conversion of the bilinear system into an equivalent linear model (ELM) by an accurate approximation of the state in the bilinear term using a set of sine and cosine basis functions whose frequencies are obtained as combinations of the input frequencies. Observer/Kalman Filter Identification (OKID), a linear time invariant (LTI) system identification algorithm, is used to identify the aforementioned ELM from which the original bilinear model is recovered. A numerical example is also provided.