Observer-Based Controllers for Incrementally Quadratic Nonlinear Systems With Disturbances

• 成果类型: Article
• 署名作者: Xu, Xiangru; Acikmese, Behcet; Corless, Martin J.
• 署名单位: University of Wisconsin System; University of Wisconsin Madison; University of Washington; University of Washington Seattle; Purdue University System; Purdue University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2020.2996985
• 发表日期: 2021
• 页码: 1129-1143
• 关键词: Nonlinear systems; observers; Linear matrix inequalities; Symmetric matrices; Closed loop systems; Output feedback; control design; Event-triggered control (ETC); incrementally quadratic nonlinearity; observer-based control; stabilization of nonlinear systems

摘要

Robust global stabilization of nonlinear systems by observer-based feedback controllers is a challenging task. This article investigates the problem of designing observer-based stabilizing controllers for incrementally quadratic nonlinear systems with external disturbances. The nonlinearities considered in the system model satisfy the incremental quadratic constraints, which are characterized by incremental multiplier matrices and encompass many common nonlinearities. The simultaneous search for the observer and the controller gain matrices is formulated as a feasibility problem of linear matrix inequalities, for two parameterizations (i.e., the block diagonal parameterization and the block antitriangular parameterization) of the incremental multiplier matrices, respectively. The closed-loop system implementing the observer-based feedback controller is proven to be input-to-state stable with respect to external disturbances. Using the proposed continuous-time observer-based controllers, event-triggered controllers with time regularization are constructed for globally Lipschitz systems, such that the closed-loop system is Zeno-free and input-to-state practically stable.