College of Information Science and Engineering, State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University, Shenyang 110819, China; College of Mathematics and Statistics, Zhoukou Normal University, Zhoukou, 466001, China.
College of Information Science and Engineering, State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University, Shenyang 110819, China.
ISA Trans. 2019 Mar;86:98-109. doi: 10.1016/j.isatra.2018.10.031. Epub 2018 Oct 25.
A framework of regional passivity theory for switched systems is set up using multiple barrier storage functions. The "energy" stored in each subsystem is described by the corresponding individual barrier storage function which is only well defined on an open region associated with regional passivity. The key feature is that the "energy" grows to infinity when the trajectory tends to the region boundary. Firstly, a sufficient condition guaranteeing regional passivity for a switched system is derived under the designed switching law, where all subsystems are not assumed to be regionally passive. Secondly, asymptotic stability can be reached if a switched system is strictly regionally passive or regionally passive plus asymptotic detectability, and meanwhile the system trajectory remains in the corresponding open region. Thirdly, regional passivity is also shown to be preserved under feedback interconnection. Finally, as an application of the theory provided, the stabilization problem for state-constrained strict-feedback switched nonlinear systems is solved, where no subsystem is required to be stabilizable.
建立了一个使用多个障碍存储函数的切换系统区域被动性理论框架。每个子系统存储的“能量”由相应的单个障碍存储函数来描述，该函数仅在与区域被动性相关的开放区域内有明确定义。关键特征是，当轨迹趋于区域边界时，“能量”会无限增长。首先，在设计的切换律下，导出了一个切换系统保证区域被动性的充分条件，其中不假设所有子系统都是区域被动性的。其次，如果切换系统是严格区域被动性或区域被动性加渐近可检测性，并且同时系统轨迹保持在相应的开放区域内，则可以达到渐近稳定性。第三，还证明了反馈互联下的区域被动性保持。最后，作为所提供理论的应用，解决了状态约束严格反馈切换非线性系统的镇定问题，其中不需要要求任何子系统是可镇定的。
