Abstract: Engine speed control system is a complex time-delay uncertain system. In this paper, a combined observer and stated feedback controller design procedure for this system is proposed. Using the engine mechanical principle, the mathematical model is established as well as the Luenberger-observer. A sufficient condition for robust asymptotical stability of the closed-loop system is presented based on Lyapunov function theory. By using matrix’s Singular Value Decomposition（SVD） and Linear Matrix Inequality（LMI） techniques, the existence condition and method of designing an observer-based feedback controller is derived. The result is obtained in terms of LMI, which makes all the gain matrices can be easily obtained by Matlab’s LMI toolbox. The simulation results demonstrate the validity of this approach.

Key words: time-delay uncertain systems, observer, feedback, Singular Value Decomposition（SVD）, Linear Matrix Inequality（LMI）

摘要： 针对发动机怠速控制系统时滞、不确定性等特点，提出一种基于状态观测的状态反馈控制方法。根据发动机力学原理建立发动机数学模型，并给出Luenberger型状态估计;基于Lyapunov泛函理论，给出闭环系统鲁棒渐近稳定的充分条件。进一步，运用矩阵奇异值分解（SVD）和线性矩阵不等式（LMI）方法，获得观测-状态反馈控制器参数的求解方法。所得结果以LMI形式给出，可以方便地利用Matlab工具箱求解。通过数值仿真，表明该方法的有效性。

关键词: 时滞不确定系统, 观测器, 反馈, 奇异值分解（SVD）, 线性矩阵不等式