Robust and resilient stabilization and tracking control for chaotic dynamical systems with uncertainties

In this article, a robust resilient design methodology for stabilization and tracking control for a class of chaotic dynamical systems is proposed. In particular, a resilient quasi-sliding mode control law is formulated to suppress the chaotic behaviour of these dynamical systems, while considering uncertainties in control input. By using Lyapunov stability theory, sufficient conditions are derived in terms of Linear Matrix Inequalities (LMIs) for a more general class of chaotic nonlinear dynamical systems satisfying the Lipschitz continuity condition. The control gains are obtained via LMI technique in the presence of bounded additive uncertainties in control input. Numerical simulations are provided for Chua's circuit, Lorenz system, and 4D Lu hyper-chaotic system to show the supremacy and effectiveness of the proposed design methodologies.