不确定时滞线性系统的鲁棒镇定问题

Robust Stabilization Problems for Uncertain Time-Delay Linear Systems

针对过程控制中普遍存在的时滞和不确定现象,应用Lyapunov稳定方法和Riccati方程方法研究了存在滞后的不确定线性系统的鲁棒镇定问题,其中的不确定性是时变有界的,不要求满足“匹配条件”;获得了一类不确定线性时滞系统用状态反馈控制器进行鲁棒镇定的充分条件.该充分条件以线性矩阵等式存在对称正定解的形式给出,通过求解代数Riccati方程的对称正定解构造线性状态反馈稳定化控制器.最后给出了算例,结果证明了对于不确定线性时滞系统,应用该方法构造的线性状态反馈稳定化控制器,可使闭环系统渐近稳定.

The problem of robust stabilizing uncertain linear systems is considered for the timedelay and uncertain phenomena widely existing in the process control. By using Lyapunov stability and Riccati equation, the sufficient condition that the uncertain linear time-delay systems can be stabilized with a state feedback controller is derived. The uncertainties under consideration are time-delay and bounded and do not meet the ＂match conditions＂. The sufficient condition is that a linear matrix equation has a positive symmetry solution. The design of state feedback controller can be obtained by solving an algebraic Riccati equation. Numerical example based on the design is given. The results show that the state feedback controller based on the design can make the closed-loop system asymptotically stable. Therefore, the effectiveness of the proposed design is verified.