滞后广义系统基本理论中的变结构控制法

Variable Structure Control of Basic Theory of Singular Systems with Delay

讨论一类带滞后的线性时变广义系统解的整体存在唯一性问题。由于这类系统的解在运动过程中会出现新的相容性条件,故解的整体存在唯一性难以满足。寻求一种新的途径,即变结构控制方法来确保系统解的运动过程中出现的新的相客性条件成立,从而保证系统初值问题连续解的整体存在唯一性。这种方法也可用于处理微分方程的边值问题。

Global existence and uniqueness of solutions is discussed for a class of linear time-varying singu-lar systems with delay. Because there are some new consistency conditions arised in the moving of solutions of the systems, it is difficult that the global existence and uniqueness of solutions is satisfied. By using the method of varible structure control, this paper makes sure that the new consistency conditions hold , and that global existence and uniqueness of continuous solutions is satisfied for the initial value problems of the sys-tems. The method can be used in discussing boundary value problems of differential equations.