基于LMI方法的时滞分布参数控制系统的镇定

LMI-based approach for stabilization of distributed parameter control systems with delay

针对常时滞、多个常时滞及多个变时滞的分布参数控制系统,提出一种与现有研究分布参数控制系统不同的方法.该方法通过构造平均Lyapunov函数,利用LMI和矩阵不等式知识,在只要求系统本身所固有的系数是负定矩阵的条件下,给出了所研究的分布参数系统镇定的充分条件.当模型中时滞为常时滞时,所得的充分条件与时滞无关;当模型中时滞为变时滞时,所得模型的镇定准则依赖于时滞.此外,该方法一个显著优点是所获得的条件容易检验,因而易于应用.

A method is proposed for the distributed parameter control systems with constant delays or time-varying delays. By constructing even type Lyapunov functions, and employing matrix inequality and LMI, a number of sufficient conditions for these types of stabilization are derived. For the case of constant time delays, the stabilization criteria are delay-independent; for the case of time-varying delays, the stabilization criteria are delay-dependent. In addition, the distinct advantage of the method is that the criteria are easy to be checked, and can be applied to-practice easily.