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 differential equations, a new criterion is derived for designing the controller gains for stabilization and tracking, in which control parameters can be selected via the pole placement technique of linear control theory. More importantly, according to our numerical studies, this method is robust against system parametric variations, can strongly reject external constant disturbances, 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.