中文摘要：

用等时区方法确定最速离散二阶系统的线性区域的边界,以开关曲线和边界线来界定控制量的线性变化,区分可达区和线性区,得到最速系统综合函数,并依此构造线性函数形式的跟踪微分器.仿真结果表明,所提出的跟踪微分器具有快速跟踪输入信号、无颤振、无超调的特点,能得到较好的微分信号,算法简洁实用.

英文摘要：

The boundary characteristic curve of linear regions with the second-order discrete time optimal control is presented by means of the isochronous region. Then the control variable is linearized, which is decided by the switching curve and the boundary curve, and the reachable region and the boundary region are given. The linear synthetic functions are obtained. Based on this function, the discrete form of tracking-differentiator is constructed. Numerical simulation shows that, this discrete form of tracking-differentiator can quickly track an input signal without overshooting and chattering, and can acquire an excellent differential signal. It is simple and practical.