多变量线性时延系统的稳定性分析及应用

Application and Stability of Multi-variable Linear Delayed Systems

基于Lyapunov稳定性理论,推导出多变量线性时滞系统的时滞独立稳定充分条件方程式,并给出了定理的另一种表述形式.在此基础上,给出了几个判定线性时滞系统独立稳定的简单判据.还讨论了时滞系统的指数稳定性,给出了系统具有任意指定收敛速度指数稳定的充分条件及相应的推论.在使用这些条件时,只需选取一组合适的参数即可降低条件的保守性.通过实例计算和对文中方法与文献中的方法进行比较表明,文中方法具有较小的保守性。

Based on Lyapunov’s stability theory,analyze on a control process of oil-water separation with time-delay,coupling and uncertainty in the unite station.An equation of sufficient condition for multi-variable linear delayed systems with delayed independent stabilization is derived and another forms are also given.Based on this,several simple criterions for judging independents stabilization from linear delayed system are presented.The exponential stability for delayed system is discussed and the sufficient condition of exponential stability with any appointed convergent rate and its corresponding deductions also are provided.Using these conditions,a set of suitable parameters to reduce the conservation can be choosed.By calculating and being compared with methods of the literature,the results show that the methods are less conservative.