Cong Wang , Li Li , Minghui Yao , Qiliang Wu , Yan Niu
{"title":"Stability analysis of generalized second-order nonlinear control systems","authors":"Cong Wang , Li Li , Minghui Yao , Qiliang Wu , Yan Niu","doi":"10.1016/j.jfranklin.2025.107606","DOIUrl":null,"url":null,"abstract":"<div><div>To overcome the constant boundedness and slow time-varying constraints of disturbances, this paper presents a generalized second-order nonlinear control algorithm (GSONCA) and resulting a generalized second-order nonlinear control system (GSONCS), and further studies the stability and disturbance rejection of GSONCS. Unlike existing similar works, the GSONCS is a universal second-order system framework including nonlinear, time-varying, and switching terms, which is able to deal with time-dependent and state-dependent disturbances. All possible equilibrium points are discussed for the GSONCS, and the existence condition of a unique equilibrium point is constructed. Several practical stability inequalities of coefficients are established for the GSONCS where the coefficients can be almost arbitrary functions of state variable and time, which unify the stability criterion of second-order linear and nonlinear systems. Based on the proposed stability results, the disturbance rejection conditions of GSONCS are derived, and the good robustness of state-dependent-type second-order nonlinear systems is confirmed. As the applications of GSONCS, the parameter tuning methods of popular second-order algorithms are provided, and simulations on DC-DC converters are presented to validate the proposed GSONCA.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"362 6","pages":"Article 107606"},"PeriodicalIF":3.7000,"publicationDate":"2025-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of The Franklin Institute-engineering and Applied Mathematics","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0016003225001000","RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"AUTOMATION & CONTROL SYSTEMS","Score":null,"Total":0}
引用次数: 0
Abstract
To overcome the constant boundedness and slow time-varying constraints of disturbances, this paper presents a generalized second-order nonlinear control algorithm (GSONCA) and resulting a generalized second-order nonlinear control system (GSONCS), and further studies the stability and disturbance rejection of GSONCS. Unlike existing similar works, the GSONCS is a universal second-order system framework including nonlinear, time-varying, and switching terms, which is able to deal with time-dependent and state-dependent disturbances. All possible equilibrium points are discussed for the GSONCS, and the existence condition of a unique equilibrium point is constructed. Several practical stability inequalities of coefficients are established for the GSONCS where the coefficients can be almost arbitrary functions of state variable and time, which unify the stability criterion of second-order linear and nonlinear systems. Based on the proposed stability results, the disturbance rejection conditions of GSONCS are derived, and the good robustness of state-dependent-type second-order nonlinear systems is confirmed. As the applications of GSONCS, the parameter tuning methods of popular second-order algorithms are provided, and simulations on DC-DC converters are presented to validate the proposed GSONCA.
期刊介绍:
The Journal of The Franklin Institute has an established reputation for publishing high-quality papers in the field of engineering and applied mathematics. Its current focus is on control systems, complex networks and dynamic systems, signal processing and communications and their applications. All submitted papers are peer-reviewed. The Journal will publish original research papers and research review papers of substance. Papers and special focus issues are judged upon possible lasting value, which has been and continues to be the strength of the Journal of The Franklin Institute.