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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。
The global existence and uniqueness of solutions for a class of linear time-varying singular systems with delay is discussed. Because of the new compatibility conditions of solutions of such systems in the process of movement, the existence and uniqueness of the solutions are difficult to satisfy. Seek a new approach, that is, the variable structure control method to ensure that the new phase conditions that occur during the motion of the system are satisfied, so as to ensure the existence and uniqueness of the continuous solutions of the system initial value problem. This method can also be used to deal with the boundary value problems of differential equations.