LMI-based Global Sliding Mode Control Scheme for Time-delayed Chaotic Systems with Input Nonlinearity

This paper proposes an LMI-based global sliding mode control approach (GSMC) for chaotic systems. The design aims at stabilizing chaotic systems with nonlinear inputs and uncertain time-delays. The proposed GSMC control algorithm is formulated using the stabilization theory of Lyapunov-Krasovskii and the linear matrix inequality (LMI)-based asymptotic stability conditions. A Wang-Chen chaotic system was considered to validate the design. The obtained results demonstrated the validity and performance of the proposed approach. Robustness against external disturbances, nonlinear inputs and time-delays along with the reduced chattering as a result of the elimination of the reaching phase are some of the significant features of the proposed approach.