中文摘要：

提出线性多变量系统控制Lyapunov函数（CLF）构造的一股方法．先证明可以通过解一类Lyapunov方程，得到线性系统二次型的CLE接着证明了对于线性系统，这种方法可以提供所有二次型的CLE最后证明了若线性系统存在CLF，那么必存在二次型的CLE由此完全解决了线性系统的CLF构造问题．

英文摘要：

A universal method for constructing control Lyapunov functions （CLF） for a linear multivariable system is presented. Firstly, we show that every quadratic control Lyapunov function can be obtained by solving the Lyapunov equation. Then, we prove that this method can generate all quadratic control Lyapunov functions for a given linear system. Finally, it is shown that if there is a control Lyapunov function then there must be a quadratic control Lyapunov function. Thus, the problem of constructing control Lyapunov functions for linear systems is solved completely.