Sliding PI controller designs with integral sliding surface for a class of nonlinear systems

In the paper, the Lyapunov stable theory and L₂-gain control performance are employed to interpret a sliding controller design with the proportional-integral (PI) control form and the integral sliding surface. First, a theoretical analysis of the considered sliding PI controller is provided. Our analysis reveals that the proportional control term of the sliding PI controller, i.e., sliding proportional controller, can lead the energy of system state error to be bounded and thus, the system fundamental robustness can be established. The integral control term of the sliding PI controller, i.e., sliding integral controller, can guarantee the system stability further. Secondly, a direct adaptive design is further proposed to estimate the optimal proportional gain of the sliding proportional controller, in which the sliding integral controller is employed to handle the total uncertainty with unknown upper bound in the adaptive control design. Therefore, the selection problem of the proportional gain is resolved and the valuable robust control property of the sliding integral controller is illustrated again. Finally, three simulations are provided to demonstrate these results.