Brief Paper - Modified adaptive backstepping design method for linear systems

In this study, a modified adaptive backstepping control is proposed for linear time-invariant (LTI) single-input single-output (SISO) plants. By introducing arbitrary-order finite-time convergence exact differentiators, the explosion of complexity problem in backstepping control is eliminated and the tracking error converges to zero asymptotically. Furthermore, the adaptive laws are necessary only at the first design step, which significantly reduce the design procedure. It is proved that, with the proposed scheme, all the closed-loop signals are semi-globally uniformly ultimately bounded. Simulation results are presented to demonstrate the effectiveness of the proposed scheme.