Robust Stability and Stabilization of Systems with Real Parameter Uncertainty

该方案解决了系统与控制领域的一个重要问题：面对不确定性的控制系统的分析与设计。针对不确定性设计控制系统的问题具有重要的实际意义，并且一直是控制理论和技术发展的主要推动力。本课题的研究内容包括在存在真实的、可能的非线性/时变不确定性时的稳定性分析、稳定化和干扰抑制。这些问题中的每一个都是独立的兴趣，它们一起遵循一个自然的进程，朝着分析和设计不确定系统的一般方法的发展。本文的主要研究对象是一个用线性分数阶变换描述的不确定动力系统，研究所需的工具包括先进的矩阵理论、凸优化技术和现代鲁棒控制理论。这里提出的方法和想法被认为是独特的和原创的。特别是，将凸优化与先进分离原理相结合，并采用参数相关增益调度控制器，对具有结构非线性/时变不确定性的系统进行镇定的方法，显得非常有前途。并有望在高度复杂不确定系统的实际设计中得到有价值的应用。

This proposal addresses an important problem in system and control area: the analysis and design of control systems in the face of uncertainty. The problem of designing a control system against uncertainties is of fundamental practical interest and has been the main thrust for development of control theory and technology. The proposed research on this subject includes stability analysis, stabilization, and disturbance rejection in the presence of real, possible nonlinear/time varying, uncertainties. Each of these problems is of independent interest and they together follow a natural progression toward the development of a general methodology for analysis and design of uncertain systems. The main object under here will be an uncertain dynamical system described by a linear fractional transformation, and the necessary tools required for this research include advanced matrix theory, convex optimization techniques, and modern robust control theory. The approaches and idea proposed here are believed to be unique and original. In particular, the proposed approaches for the stabilization of systems with structured nonlinear/time varying uncertainty using the combination of convex optimization and advanced separation principle, and using the parameter dependent gain scheduled controller, appear very promising, and are expected to lead to valuable applications in practical design of highly complex uncertain systems.