广义连续系统的鲁棒H∞控制及仿真

摘要

For a class of uncertain generalized continuous linear systems with time-invariant norm-bounded parameter uncertainties, the state feedback robust H-infinity control hard problem was resolved. A sufficient condition for the solvability of the problem and the state feedback robust H-infinity feedback controller were obtained in terms of liner matrix inequalities. The result deepened the content of robust H∞ control theory, and it simplified some past methods. The designed controller not only guaranteed that the closed-loop systems was regular, causal, stable but also satisfied a prescribed H-infinity norm bounded constraint for all admissible uncertain parameters under some conditions. A real project simulation example was given to demonstrate the effectiveness of the proposed method.%针对一类具有时不变的、模有界参数不确定性的广义连续系统,为了解决系统的状态反馈鲁棒H∞控制的难点问题,利用线性矩阵不等式(LMI)的方法,得到了问题可解的条件,并给出了相应的状态反馈控制律.得出的定理不仅深化了鲁棒H∞控制理论,并简化了以往的方法.在一定条件下,所采用的状态反馈鲁棒H∞控制律不仅对广义连续系统对所有容许的不确定性参数,也能够保证闭环系统正则、具有因果关系并且控制稳定,同时对传递函数矩阵能够满足给定的H∞性能指标.经过实际工程算例仿真验证了定理的正确性.