This paper addresses the stabilization issue of linear time delay system with input saturation and distinct input delays via predictor feedback boundary control algorithm by employing transport partial differential equations (PDEs). First, the addressed ordinary differential equation (ODE) system with input delay is equivalently represented as a cascade of an ODE and transport PDEs. Second, by employing the backstepping Volterra integral transformation technique, the equivalent cascade system is transformed into a stable target system, whose kernels are solved by the constraints satisfying transport PDEs. Third, based on the boundary conditions of the obtained invertible transformation, the proposed feedback control law can be formulated. Fourth, by applying semigroup operator theory, the well-posedness of the resulting system is proved and consequently, novel exponential stability conditions of the addressed system are established. Then, the domain of attraction region under the given actuator saturation constraints is estimated with the help of the solution of obtained stability conditions. Finally, a demonstrative simulation example is offered to verify the feasibility and usefulness of the results.

本文通过采用传输偏微分方程 (PDE) 的预测器反馈边界控制算法解决了具有输入饱和和不同输入延迟的线性时延系统的稳定性问题。首先，具有输入延迟的寻址常微分方程 (ODE) 系统等效地表示为 ODE 和传输 PDE 的级联。其次，通过采用反步 Volterra 积分变换技术，等效级联系统被转化为一个稳定的目标系统，其内核由满足传输偏微分方程的约束求解。第三，基于所获得的可逆变换的边界条件，可以制定所提出的反馈控制律。第四，应用半群算子理论，证明了所得系统的适定性，从而建立了所解决系统的新指数稳定性条件。然后，借助获得的稳定性条件的解，估计给定执行器饱和约束下的吸引力区域域。最后，给出了一个示范性的仿真例子来验证结果的可行性和有用性。