A new variable structure control law for non-linear plant with uncertainties

In this paper, a new variable structure control law that is called logic and extreme control law is proposed for nonlinear single-input time-variant plants with matched or mismatched uncertainties. Its design method, which is totally based on the plant ideal model and the uncertainties' extreme values, is also studied. Meanwhile, some direct and general relations between the uncertainties and the control laws' parameters are established. No matter what concrete forms the uncertainties have, the control law designed ensures that the sliding mode exists and the closed loop control system is asymptotically stable or ultimately bounded. The results got in this paper are suited to many areas, such as guided missiles, aircrafts and satellites.