Control of uncertain butterfly-shaped chaotic system: Sliding-mode approach

A sliding mode control scheme for an uncertain butterfly-shaped chaotic dynamical system is proposes in this paper. A sliding surface is determined according to the sliding mode control technique and the control law is established. Stability of the sliding control law is determined using Lyapunov stability theory. The chattering phenomenon, which deteriorates the system performance and may cause unforeseen instabilities, is attenuated due to this control law. The effectiveness of the presented sliding mode control design is confirmed through numerical simulations.