Robust absolute stability of Lur'e control systems in parameter space

This paper deals with the problem of robust absolute stability analysis for nonlinear Lur'e control systems in the presence of system parameter variations. The well known Popov criterion for absolute stability is used in order to characterize the boundary of the region of absolute stability in the parameter plane when the coefficients of the transfer function of the linear plant are polynomial functions of the uncertain parameters. For a scalar parameter, a method is given to determine the maximal interval of variation around a fixed nominal value preserving absolute stability. This result is also used to derive a technique for checking absolute stability of Lur'e systems with parameters in given planar uncertainty sets. Numerical examples showing the application of the method are reported.