Robust Stabilization of Linear Differential Inclusion Using Adaptive Sliding Mode Control

Abstract

Control of the linear polytopic Differential Inclusion system in the presence of bounded disturbance is studied. An adaptive sliding mode control is proposed to achieve the asymptotic stability of the differential inclusion systems. The convergence conditions of the dynamics of sliding mode to zero and adaptive rules to update the control signal are derived. A new Lyapunov analysis-based theorem is formulated that proves the states' convergence to zero. Finally, the efficiency of the proposed control is illustrated via simulations of a numerical linear polytopic differential inclusion system.