中文摘要：

由为矩形的描述符系统的动态赔偿的线性二次的最佳的控制在这份报纸被考虑。首先，有一份合适的动态订单的一个动态赔偿者被给以便靠近环的系统常规、没有推动、稳定(它被叫可被考虑) ，并且它的联系矩阵不平等和 Lyapunov 方程有一个解决方案。另外，二次的性能索引在与解决方案和靠近环的系统的起始的值有关的一种简单形式被表示。以便为系统解决最佳的控制问题，建议 Lyapunov 方程被转变成一个双线性的矩阵不平等(BMI ) ，和一个相应路径追随者算法在一个最佳的动态赔偿者能在哪个被获得被建议最小化二次的表演索引。最后，一个数字例子被提供表明建议途径的有效性和可行性。

英文摘要：

The linear-quadratic optimal control by dynamic compensation for rectangular descriptor system is considered in this paper.First,a dynamic compensator with a proper dynamic order is given such that the closed-loop system is regular,impulse-free,and stable（it is called admissible）,and its associated matrix inequality and Lyapunov equation have a solution.Also,the quadratic performance index is expressed in a simple form related to the solution and the initial value of the closed-loop system.In order to solve the optimal control problem for the system,the proposed Lyapunov equation is transformed into a bilinear matrix inequality（BMI）,and a corresponding path-following algorithm to minimize the quadratic performance index is proposed in which an optimal dynamic compensator can be obtained.Finally,a numerical example is provided to demonstrate the effectiveness and feasibility of the proposed approach.