Stabilizing unstable equilibrium points of a class of chaotic systems using a state PI regulator

In this brief, the state PI regulator method is introduced for stabilizing unstable equilibrium points and tracking set-point targets for a class of chaotic systems. Based on the theory of nonlinear ordinary dif- ferential equations, a new criterion is derived for designing the controller gains for stabilization and tracking, in which control parameters can be se- lected via the pole placement technique of linear control theory. More im- portantly, according to our numerical studies, this method is robust against system parametric variations, can strongly reject external constant dis- turbances, and possesses an attractive low-frequency-disturbance response property. The design method is applied to the chaotic Lorenz system and Chua's circuit with a cubic nonlinearity, showing satisfactory simulation results.