Sliding mode control for singularly perturbed linear continuous time systems: Composite control approaches

We investigate the problem of sliding mode control for singularly perturbed systems with external disturbances. Although the system can be decoupled into two time-scales in terms of two lower dimensional state vectors, the similar type of decomposition does not hold for the control law and the disturbance. The system decoupling transformation can only decompose the control law and the disturbances into two time-scales but not reduce their dimensions. Therefore, only one subsystem is designed to enter the sliding mode. Two composite control approaches are proposed to handle the stability and disturbance rejection problems: state feedback control used to stabilize slow or fast modes and discontinuous control used to deal with the remaining modes. A numerical example of a longitudinal model of an F8 aircraft is provided to illustrate the efficiency of the proposed methods.