基于RLS的改进双线性模型的稳定性分析

Stability Analysis for a Modified Bilinear Model Based on Recursive Least Squares

双线性多项式的非线性特征只能靠输入-输出交叉项表达,无法精确地表达高阶非线性系统.为此,对改进双线性多项式模型的稳定性进行了研究.利用迭代最小二乘法辨识改进双线性模型的参数,在复数域中,推导该算法的迭代公式,并验证了系统模型的稳定性.结果表明,通过迭代最小二乘法辨识得到的系统模型为有界输入-有界输出稳定.

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.