Although most of the control design methods assume unbounded control signals, real systems do have saturating actuators, which may degenerate closed-loop performance or even lead to unstable behavior. Additionally, the delay is generally almost ubiquitous in processes, that is also imposing performance and stability constraints. Our main contribution is to provide a controller design methodology for the stabilization of delayed systems under saturating actuators. Specifically, we address the design of non-Parallel Distributed Compensation (non-PDC) state feedback fuzzy control laws that locally stabilize a class of nonlinear discrete-time systems with state time-varying delay and saturating actuators. The proposed non-PDC control law depends on the current state x_k and the state delayed by $\overline{d}$ samples. Based on the Lyapunov–Krasovskii approach, we characterize the safe region of initial conditions through two sets: an ellipsoidal one for the current state vector, and another set for the delayed state vectors. Through two convex optimization procedures, we can maximize the estimate of the region of attraction of the closed-loop control system. Additionally, a relaxation method inspired by the Frank-Wolfe algorithm is introduced, yielding better estimates of the region of attraction. The achievements are compared with other finds in the literature, illustrating the efficiency of this proposal.

尽管大多数控制设计方法都假定无限制的控制信号，但实际系统确实具有饱和的执行器，这可能会使闭环性能退化甚至导致不稳定的行为。另外，延迟通常在过程中几乎无处不在，这也施加了性能和稳定性约束。我们的主要贡献是为饱和驱动器下的延迟系统的稳定化提供一种控制器设计方法。具体来说，我们解决了非并行分布式补偿（non-PDC）状态反馈模糊控制定律的设计问题，该定律可以局部稳定一类具有状态时变延迟和饱和执行器的非线性离散时间系统。拟议的非PDC控制律取决于当前状态x _k和延迟状态$\overline{d}$样品。基于Lyapunov–Krasovskii方法，我们通过两个集合来表征初始条件的安全区域：一个椭圆形的集合用于当前状态向量，另一个集合用于延迟的状态向量。通过两个凸优化程序，我们可以使闭环控制系统的吸引区域的估计最大化。此外，还引入了一种受Frank-Wolfe算法启发的松弛方法，可以更好地估计吸引区域。将这些成就与文献中的其他发现进行比较，说明了该建议的有效性。