多平衡点线性切换系统反馈实用镇定设计及其应用

Aiming at the scientific problem of the practical stabilization about the given region for the switched linear systems with different equilibrium point for each subsystem and the number of subsystems is not larger than the system’s dimension, the influencing mechanism of switching law on integer switched systems, the practical stability criterion on fixed region, as well as the design of the well-defined output feedback switching law are focused in this project. The integer switched system is applied to approximately depict the dynamic and characteristics of switched linear system on fixed region. By means of geometrical analysis method and Lyapunov-like function, the less conservative criterion on practical stability for integer switched systems and switched linear systems are sought. Based on the direct Lyapunov method and the partition of the state space, the practical stable feedback switching law are pursued. By extending the slow-switching technology, combined with the observer design methods and separation principle, a well-defined and output feedback switching design strategy is conducted. The achievements of the project are expected to enrich the stability analysis method for integer systems, diverse the practical stability design scheme, and provide a theoretical basis for realizing the practical stability of multi-equilibrium switched linear systems.

针对各子系统平衡点不同且子系统数量不多于系统维数时线性切换系统实用镇定问题, 本项目开展切换律对积分切换系统实用稳定性影响机制、多平衡点线性切换系统关于给定区域实用可镇定判据、基于输出反馈且具良定性切换律设计三方面研究. 采用积分切换系统近似描述指定域内多平衡点线性切换系统的运动规律, 结合几何分析和Lyapunov函数法, 发展积分切换系统、多平衡点线性切换系统统一且低保守性实用可镇定判据; 利用Lyapunov直接法、状态空间划分策略, 探索状态反馈实用稳定切换律设计方法; 采用慢切换技术, 结合观测器设计方法及分离原理, 获得良定且基于输出反馈的实用镇定性设计框架. 研究结果将为积分系统实用稳定性分析提供新思路, 为实用镇定控制律设计提供新方法, 为实现多平衡点线性切换系统实用稳定控制提供研究基础.

本项目针对各子系统平衡点不同且子系统数量不多于系统维数时线性切换系统的实用镇定问题, 展开了基于输出反馈且具良定性切换律对多平衡点线性切换系统关于给定区域实用可镇定影响的研究. 通过积分切换系统近似描述指定域内多平衡点线性切换系统的运动规律, 结合几何分析和Lyapunov函数法, 探究了多平衡点线性切换系统统一且低保守性实用可镇定判据; 采用慢切换技术, 结合观测器设计方法及分离原理, 获得了良定且基于输出反馈的实用镇定性设计框架. .本项目扩充和深化了切换系统理论, 研究成果在电力电子装置, 汽车悬架系统控制, MEMS微镜控制等实际应用中有着广泛的应用前景.