中文摘要：

针对线性矩形广义系统，研究了基于动态补偿的有限时域模型预测控制问题，给出了存在合适维数的动态补偿器使得闭环系统正则、无脉冲、稳定的充要条件．在有限时域性能指标中引入一个终端有限权矩阵来保证稳定性，并利用矩阵不等式和Lyapunov方程求解优化问题，将提出的Lyapunov方程转化为双线性矩阵不等式形式（BLMI），以便采用路径算法最小化性能指标，保证了闭环系统是容许的．数值算例验证了方法的有效性．

英文摘要：

The finite-horizon model predictive control by dynamic compensation for rectangular descriptor system is considered. A dynamic compensator with a proper dynamic order is given such that the closed-loop system is regular, impulse-free, stable. A terminal weight matrix is introduced in the performance to ensure the stability, and matrix inequlity and Lyapunov equation is utilized in order to solve the optimal problem. The proposed Lyapunov equation is transformed into a bilinear matrix inequality, then a path-following algorithm is used to minimize the performance index. At last, a numerical example is given to illustrate the effectiveness of the controller.