Passivity-based fractional-order integral sliding-mode control design for uncertain fractional-order nonlinear systems

• Passivity-based fractional-order (FO) integral sliding mode controller is proposed for FO nonlinear systems.
• The effects of model uncertainties and an exogenous input are taken into account in the design procedure.
• The passivity notion is extended for FO systems.
• A parameter adjustment scheme for FO integral sliding surface is proposed by using the linear matrix inequality (LMI) approach.
• Stability and reachability analysis for the closed loop system is discussed based on the fractional Lyapunov theory.

This paper concerns with the problem of designing a passivity-based fractional-order (FO) integral sliding mode controller for uncertain FO nonlinear systems. Utilizing the FO calculus, it is showed that the state trajectories of the closed-loop system reach the FO switching manifold in finite time. The control law ensures the asymptotical stability on the sliding surface. A parameter adjustment scheme for FO integral sliding surface is proposed by using the linear matrix inequality (LMI) approach. The proposed controller can be applied to different systems such as chaotic systems. Finally, simulation results are provided to show the effectiveness of the proposed method controlling chaos in FO Chua circuit and FO Van-der-Pol oscillator.