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在同时考虑系统矩阵参数不确定性和控制器不确定性对系统性能影响的前提下,研究了一类基于观测器的不确定广义时滞系统的弹性保成本控制问题。基于Lyapunov稳定性理论,通过构造广义Lyapunov函数和广义二次性能指标函数,以线性矩阵不等式的形式给出了基于观测器状态反馈的弹性保成本控制器的设计方法。该控制器不仅保证了广义时滞系统是鲁棒稳定而且使其具有相应的性能指标上界。采用一种新方法将系统弹性保成本控制器设计和状态观测器增益矩阵求取转化为两组严格线性矩阵不等式的可行解问题。最后通过算例验证了该方法的可行性和有效性。
Considering the uncertainties of the system matrix parameters and the controller uncertainties on the performance of the system, a class of observer-based elastic guaranteed cost control of uncertain singular time-delay systems is studied. Based on the Lyapunov stability theory, a generalized Lyapunov function and a generalized quadratic performance index function are used to design an elastic guaranteed cost controller based on observer state feedback in the form of linear matrix inequalities. The controller not only guarantees that the generalized time-delay system is robust and stable, but also has the corresponding upper bound of performance index. A new method is used to convert the system guaranteed cost controller design and state observer gain matrix into a feasible solution to two strict linear matrix inequalities. Finally, an example is given to verify the feasibility and effectiveness of the method.