关于线性系统时间最优控制的切换次数

Switch degree of time optimization control in linear system

线性系统时间最优控制的切换问题在许多实际工程中起着重要的作用,文献[1]和文献[2]中对之都进行了讨论,但是他们只讨论了系统矩阵A的特征值为互异实数的情形。作者经过研究,得出了当矩阵A的特征值为实数时(A为二阶、三阶)也成立的结论,此外,对A的特征值为复数情形,给出了相反的结论。

The switch problem of the time optimization control in linear system plays an important role in many practical projects.Both Literature[1] and Literature[2] have discussed the problem,but only one case in which the eigenvalues of coefficient matrix are different when real number is concerned.The author finds that the result is also tenable when the eigenvalue of A matrix(A is two-rank or three rank) is a common real number.Then,the author comes to a contrany condusion when the eigenvalue of A matrix is a complex number.