This article presents a saturation controller design method for a type of nonlinear time-delay systems. Different from the current works, the nonlinear systems considered herein satisfy an incremental quadratic constraint, which is a more general nonlinearity. Firstly, for the constraint in the actuator, the convex set theory is employed to transform the saturated feedback law into a parameterized linear convex hull set. Next, the convex hull Lyapunov function is constructed to obtain sufficient conditions for exponential stability of the closed-loop system. In addition, by solving an optimization problem, the maximal estimation of domain of attraction is also determined. Finally, numerical examples are provided to verify the proposed method.

本文提出了一种用于非线性时滞系统的饱和控制器设计方法。与当前的工作不同，此处考虑的非线性系统满足增量二次约束，这是一个更一般的非线性。首先，针对执行器中的约束，采用凸集理论将饱和反馈定律转换为参数化的线性凸壳集。接下来，构造凸包Lyapunov函数以获得足够的条件来实现闭环系统的指数稳定性。另外，通过解决优化问题，还确定了吸引域的最大估计。最后，通过数值算例验证了该方法的有效性。