不确定线性时滞系统的鲁棒镇定

Robust Stabilizing Controller for Uncertain Linear Time-Delay Systems

针对过程控制中,普遍存在的时滞和不确定现象,研究了状态和控制均存在滞后的不确定线性时滞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"。应用Lyapunov稳定性分析和Riccati方程方法,提出了不确定线性时滞系统能用无记忆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不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,来构造无记忆线性状态反馈稳定化控制器,并给出了基于该方法的数值算例,数值仿真结果表明了对于状态和控制均存在滞后的不确定线性时滞系统,应用该算法构造的无记忆线性状态反馈稳定化控制器,可使闭环系统是二次稳定的,故而证明了该算法的有效性。

The problem of robust stabilizing uncertain linear systems with both state delay and control delay is considered for the time-delay and uncertain phenomena universally-existed in the process control. The uncertainties under consideration are time-varied and bounded and do not need to meet the 'match conditions'. By using the Lyapunov stability and Riccati equation theories, the sufficient condition that the uncertain linear time-delay systems can be stabilized with a non-memory state feedback controller is derived. The sufficient condition is that a linear matrix inequation has a positive symmetry solution. The design of non-memory state feedback controller can be obtained by solving an algebraic Riccati equation. Numerical example based on the design is given. The numerical simulation results show that the non-memory state feedback controller based on the design can make the closed-loop system quadratic stable. Thus, the effectiveness of the proposed design method is testified. 