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研究了一类具有控制时滞和外部扰动的线性时不变离散系统鲁棒控H∞控制器设计问题。基于Lyapunov稳定性理论、鲁棒控制理论和线性矩阵不等式处理方法,通过构造合适的Lyapunov-Krasovskii函数,推导出闭环控制系统渐近稳定的充分条件且得出鲁棒H∞控制律和其性能指标γ,并探讨了H∞最优控制问题,给出了最优H∞控制律参数化的设计方法,最后给出网络控制实际系统的例子对所得算法进行验证,说明分析方法和结果是有效可行的。
A robust control H∞ controller design for a class of linear time-invariant discrete-time systems with controlled delays and external perturbations is studied. Based on Lyapunov stability theory, robust control theory and linear matrix inequalities, a sufficient condition for asymptotic stability of the closed-loop control system is derived by constructing an appropriate Lyapunov-Krasovskii function and the robust H∞ control law and its performance index γ, and discusses the H∞ optimal control problem, gives the optimal H∞ control law parameterized design method, and finally gives the network control of the actual system example to verify the resulting algorithm, indicating that the analysis methods and results are valid of.