A Complementary Form of Discrete Tracking-Differentiator

A synthetic function for time optimal control of the second-order discrete-time system without control constraint is derived in this paper. It is proved that by the use of the function, any non-zero initial state of the system can be driven to the origin in two steps. Based on this synthetic function, a high speed discrete tracking-differentiator with simple form is presented. Numerical simulation shows that the proposed tracking-differentiator can quickly track input signal with excellent filtering performance and produce a good differential signal of the input.