Sliding mode control of linear time-varying systems application to trajectory tracking control of nonlinear systems

This paper concerns with the sliding mode controller design method for linear time-varying systems. For this purpose, using the time-varying pole placement technique, the state feedback is designed first so that the time-varying closed loop system is equivalent to the standard linear time invariant system. Then, conventional sliding mode controller design method is applied to this time invariant system to obtain the control input. Finally, using the time-varying transformation matrix, this sliding mode control input is put back to the control input for the original system. In this paper, this controller is applied to the trajectory tracking control problem for nonlinear systems.