一类非线性状态时滞系统的基于采样控制器的渐近稳定问题

针对一类含有状态时滞的非线性系统,利用采样控制方法研究其渐近稳定问题.解决这一问题的关键在于对系统时滞的处理,以及对由于采样方法而产生的状态增长误差进行估计.由于所考虑的时滞是常时滞,可以利用分割方法对系统时滞进行分割,将时滞划分成与采样时间长度相同的数个时间区间,并基于这种分割,通过数学归纳法对系统状态增长误差进行估计.通过坐标变换引入一个比例增益压制系统的非线性项,然后设计含有比例增益的状态采样观测器和采样控制器,结合非线性时滞系统的Lyapunov泛函方法分析闭环系统的稳定性,最终确定比例增益和采样时间需要满足的条件,以保证闭环系统的渐近稳定性.最后通过数值例子表明所用研究方法以及所得研究结果是有效的.

Asymptotic stability for a class of nonlinear systems with state time-delay based on sampled-data controller

This paper studies the problem of asymptotic stability for a class of nonlinear systems with state time-delay by using sampled-data control method. The key technology to solve this problem is the dispose of time-delay, as well as the error estimate of state growth which is resulted by using sampled-data methods. Since the time delay is a constant, it can be divided into several intervals which have the same length as the sampling period. Based on this division, a mathematical induction approach is proposed to estimate the state growth. A scaling gain is introduced by coordinate transformation to deal with the nonlinear terms of the system, and then the state observer and controller are designed, which contain the scaling gain via the sampled-data control method. Combined with the Lyapunov functional method of nonlinear time-delay systems, the stability of the closed-loop system is analyzed, and finally the appropriate scaling gain and sampling period are determined to guarantee the asymptotic stability of the closed-loop system. The numerical example verifies the availability of the method and the obtained results.