A New Sliding Mode Control Approach for a Class of Nonlinear Uncertain Systems with State Time Delays

In this paper, sliding mode control (SMC) approach is proposed for the tracking control tasks of a class of nonlinear uncertain systems with state time delays. The time delay is constant and bounded. The SMC can handle matched L_infin type system uncertainties with known bounding functions. To deal with unmatched L₂ type disturbances without any information on the bound, L₂ gain is a proper performance index to analyze the disturbance attenuation level. The nonlinear uncertain systems has two cascade subsystems. The main contributions of this work are that: (i) for the first subsystem in the presence of unmatched disturbances, the switching surface is designed by solving a linear matrix inequality through achieving the delay dependent stability condition for time delay systems; (ii) the resulting sliding manifold in the sliding phase achieves the desired L₂ gain property; (iii) the SMC applied to the second subsystem can accomplish the tracking task in the existence of state time delays while ensuring the L₂ gain in the reaching phase as well. Finally, simulation examples are presented to show the effectiveness of the proposed method.