Discrete time adaptive sliding control of nonlinear systems without matching condition

This paper presents a discrete time adaptive sliding control law for SISO nonlinear systems with mismatched uncertainties. The systems are assumed to have no zero dynamics, i.e. the relative degree is the same as the system order. Control objective is for the output to track a sufficiently smooth desired trajectory. The control law utilizes the idea of the multiple sliding surface. The developed discrete time adaptation laws differ from those of conventional sliding control, and aim at adaptation on time varying parameters such as disturbances or unstructured unmodeled dynamics. The close loop stability is checked in the discrete time domain, and exponential decay of the adaptation error can be guaranteed by proper placement of the discrete time closed loop poles