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Input‐to‐state stability of switched nonlinear systems with delay in the active mode detection
Author(s) -
Motchon K.M.D.,
Etienne L.,
Lecoeuche S.
Publication year - 2019
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.4752
Subject(s) - control theory (sociology) , dwell time , lyapunov function , nonlinear system , mathematics , stability (learning theory) , state (computer science) , controller (irrigation) , polynomial , mode (computer interface) , full state feedback , exponential stability , computer science , control (management) , algorithm , physics , quantum mechanics , artificial intelligence , machine learning , operating system , medicine , clinical psychology , mathematical analysis , agronomy , biology
Summary A switched nonlinear system subject to disturbances is considered in this paper. The switching signal admits an average dwell time and a state feedback control depending on the system operating modes, detected with a maximum time delay, is applied to the system. In this framework, the input‐to‐state stability problem of the closed‐loop system is addressed. Based on some established existence conditions of mode‐dependent Lyapunov‐like functions, the values of the maximum time delay and the average dwell time that allow to achieve the input‐to‐state stability of the closed‐loop system are determined. In order to obtain more tractable results, the existence conditions of the mode‐dependent Lyapunov‐like functions are given in terms of sum‐of‐squares programming in the case of polynomial nonlinearities. In the linear case, they are expressed in terms of linear matrix inequalities and a procedure for the synthesis of the mode‐dependent controller is provided in this situation. The established theoretical results are illustrated through a control problem of a building ventilation system and a switched control problem of a vehicle suspension system.