Abstract: The nonlinearity of bilinear polynomial only relies on the input-output cross term to express; it is hard to accurately describe the system with higher order nonlinearity. For improving the performance of models, many modified bilinear polynomials are proposed. However, the complex feedback terms cause models to be unstable, which restrict the modified models to be widely used in practice. Therefore, the stability of a modified bilinear model was analyzed. Recursive least squares (RLS) is used to identify parameters of the modified bilinear model, and the iterative formulas of the algorithm are deduced in the complex field. Simultaneously, the stability of the identified system is verified. It is shown that the bilinear system model identified by RLS, has bounded-input bounded-output stability.

Key words: recursive least squares, modified bilinear model, stability