Robust prevention of limit cycle for nonlinear control systems with parametric uncertainties both in the linear plant and nonlinearity

A new method is proposed to compute all feasible robust stabilizing controllers for preventing the generation of limit cycle of nonlinear control systems with parametric uncertainties both in the linear plant and nonlinearity. The describing function analysis method is employed to approximate the behaviors of the nonlinearity. The Kharitonov theorem is utilized to characterize parametric uncertainties in the linear plant and nonlinearity. Necessary conditions for limit cycles are established. Boundaries for the generation of limit cycle and boundaries for asymptotic stability are portrayed exploiting the stability equation method. The region for prescribed limit cycle behavior and the region for asymptotic stability are located. An admissible specification-oriented Kharitonov region is found directly on the controller parameter plane. The region is non-conservative and constitutes all of the feasible controller gain sets to achieve robust prevention of limit cycle for the considered uncertain nonlinear control systems. The way to tune the controller gains is suggested. Finally, for comparison purpose, two illustrative examples proposed in the literature are given to show how the proposed algorithm can be effectively applied to tune a robust controller to achieve a prescribed limit cycle behavior and accomplish robust limit cycle amplitude suppression and prevention.