1993 Volume 6 Issue 9 Pages 416-424
We consider the stability criterion of Popov for multivariable Lur'e systems. To derive the criterion using a Liapunov function, we need to restrict the class of nonlinearity in the system. The largest class reported so far is that of differentiable nonlinearities with symmetric Jacobian matrices. In this paper, we extend the class by removing the assumption of differentiability from a part of the nonlinearity. For nonlinearities which are not in this class, the Popov criterion is not valid. Therefore, we propose modified criteria to apply to systems with such nonlinearities. To do this, we take the symmetric part of the nonlinearity as nominal and treat the residual as a perturbation.