Robust Stability and Stabilization of Continuous-Time Parameter-Varying Persidskii Systems

• 成果类型: Article
• 署名作者: Zhang, Junfeng; Combastel, Christophe; Efimov, Denis; Zolghadri, Ali
• 署名单位: Hainan University; Centre National de la Recherche Scientifique (CNRS); Universite de Bordeaux; Centre National de la Recherche Scientifique (CNRS); Inria; Universite de Lille; Institut Universitaire de France
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2025.3567675
• 发表日期: 2025
• 关键词: STATE STABILITY; input

摘要

This article investigates analysis and design problems for a class of parameter-varying generalized Persidskii systems. A model within this class is simultaneously linear in time-varying parameters as in the linear parameter-varying (LPV) framework, and contains sector nonlinearities of the state, as in Persidskii systems. The conditions for (integral) input-to-state stability and input-output-to-state stability are established. These results are developed using both, parameter-dependent and independent, Lyapunov functions. To formulate these conditions, parameterized matrix inequalities are used, which are reduced to linear ones under additional assumptions concerning the model's dependence on the time-varying parameters. Finally, a new robust nonlinear control design method is also developed. The efficacy of these results is illustrated through a numerical academic example and a more complex model describing the nonlinear dynamics of aircraft longitudinal motion.