H∞ controlling hyperchaos of the Rössler system with input nonlinearity

Based on the concept of variable structure control, this paper investigates the controller design for suppressing hyperchaos of the Rössler system with H∞ norm constraint. A proportional-integral (PI) switching surface is newly adopted so that it becomes easy to solve the H∞ control problem for such chaotic systems in the sliding mode. Based on this PI switching surface, a variable structure controller (VSC) is derived to guarantee the occurrence of sliding mode motion in finite time, even when the system is undergoing both input nonlinearity and external disturbance. Furthermore, a modified continuous controller is proposed to reduce the chattering phenomenon due to the conventional switching type VSC. An illustrative example is given to show the applicability of the proposed VSC design approach.