时滞系统是具有广泛应用背景的无限维系统，其控制在理论上极具挑战性。另外，任何控制系统的执行器都受到饱和约束，其存在使得实际系统呈现出本质的非线性特征。申请人负责的青年基金项目针对具有饱和约束与时滞的控制系统，提出了一种基于参量Lyapunov方程的控制器设计方法。目前该项目已取得阶段性的进展，发表了学术论文37篇，其中SCI论文32篇，第一作者SCI论文26篇，包括IEEE TAC长文1篇和Automatica长文2篇。本项目在青年基金项目的基础上进一步研究时滞系统的（约束）控制问题，特别地，将针对传统预估器反馈在实现上存在的问题，提出截断预估器反馈的控制思想。其核心是通过截断传统预估器反馈中的相对于名义反馈增益的高阶项而保留占主导地位的低阶项，从而能在保持传统预估器反馈的有效性的前提下，为时滞系统控制器的设计和实现带来巨大的方便，并能有效地处理饱和约束，为相关工程实践提供一定的理论指导。

Time-delay systems, which have widely applications in the practice engineering, are infinite dimensional systems whose control is challenging in theory. On the other hand, every control system is subject to actuator saturation constraint, which makes the overall practical control systems inherently nonlinear. In the previous project supported by NSFC, a parametric Lyapunov equation based approach has been developed to deal with controllers design for control systems with saturation constraints and time-delays . Progressive achievements have been made for this project by the investigator and the collaborators. By now, they have published 37 technical papers and 32 of which have been indexed by SCI. Among these publications, there are 26 first-author papers for the investigator of this project, including a regular paper on IEEE TAC and 2 regular papers on Automatica. Based on the obtained results supported by the previous NSFC project, the present project will continue to study control and constrained control problems for time-delay systems. Particularly, a novel truncated predictor feedback based approach will be established to overcome the shortcoming existing in the traditional predictor feedback approach for time-delay systems. The core idea of the truncated predictor feedback is to neglect the higher-order terms with respect to the nominal feedback gain by maintaining the lower-order dominated terms in the traditional predictor feedback. Hence the truncated predictor feedback can bring great convenience in the design and implementation of controllers for time-delay systems by inheriting the effectiveness of the traditional predictor feedback. The truncated predictor feedback approach also possesses the advantage of handling easily the saturation constraints existing in the control systems, and is expected to provide certain theoretical guidance for the related control engineering practice.