Prevention of Limit Cycle for Nonlinear Control Systems with Parametric Uncertainties

A new method is proposed to synthesize robust stabilizing controllers for preventing the generation of limit cycle of control systems with parametric uncertainties both in the linear plant and nonlinearity. Boundaries for the generation of limit cycle and boundaries for asymptotic stability are portrayed. The region for prescribed limit cycle behavior and the region for asymptotic stability are located. The overlapped region of the admissible parameter region for each Kharitonov polynomial is called the Kharitonov region. The Kharitonov region constitutes all of the feasible controller gain sets to achieve robust prevention of limit cycle. Finally, two illustrative examples are given.