Robust limit cycle amplitude suppression for a class of uncertain nonlinear control systems

A new technique is proposed to synthesize robust controller to suppress the amplitude of the limit cycle persisting in uncertain nonlinear control systems. The Kharitonov theorem is utilized to characterize the plant variations. A family of Kharitonov polynomials is obtained for limit cycle analysis. Further, by decomposing each of the vortex Kharitonov polynomial into real part and imaginary part results in two related stability equations. By solving the two stability equations, an admissible specification-oriented parameter region is found directly on the controller coefficient plane. The Kharitonov region constitutes all of the feasible controller parameter sets to achieve robust limit cycle amplitude suppression for the entire uncertain nonlinear control system. Remarkably, the controller can be designed with more flexible choice. Finally, two examples are given to show the effectiveness of the proposed technique.