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针对带有输入时滞的分数阶线性时滞系统,考虑输出反馈控制问题。首先,设计分数阶状态预估器,将分数阶时滞系统转换为新的分数阶无时滞系统;然后,设计输出反馈控制器;最后,基于Reciprocal Projection引理和线性矩阵不等式方法,给出闭环系统稳定性分析以及相应的输出反馈控制律存在的充分条件,该输出反馈控制器能够保证闭环系统的渐近稳定。给出数值算例以说明文中设计方法的有效性。
For fractional linear systems with input delay, output feedback control is considered. Firstly, fractional order state estimators are designed and the fractional order time-delay system is transformed into a new fractional order time-delay system. Then, an output feedback controller is designed. Finally, based on Reciprocal Projection Lemma and Linear Matrix Inequality, Closed-loop system stability analysis and the corresponding output feedback control law of the existence of sufficient conditions, the output feedback controller to ensure the closed-loop system asymptotic stability. Numerical examples are given to illustrate the effectiveness of the design method in this paper.