Premium
Discretized quasi‐time‐dependent ℋ ∞ control for continuous‐time switched linear systems with persistent dwell‐time
Author(s) -
Tong Yanhui,
Sun Weichao,
Li Xiaohang
Publication year - 2021
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.5444
Subject(s) - discretization , dwell time , control theory (sociology) , controller (irrigation) , lyapunov function , mathematics , reset (finance) , state (computer science) , quadratic equation , computer science , linear system , control (management) , algorithm , nonlinear system , medicine , mathematical analysis , clinical psychology , physics , geometry , quantum mechanics , artificial intelligence , financial economics , agronomy , economics , biology
This article is concerned with the dynamic output‐feedbackℋ ∞control problem for continuous‐time switched linear systems with persistent dwell‐time (PDT). Considering the quasi‐periodic property of PDT switching, a discretized quasi‐time‐dependent (QTD) control scheme is proposed by means of a multiple discretized QTD Lyapunov function approach. This control scheme is devoted to designing discretized controllers for continuous‐time switched systems straightforwardly. Firstly, the stability andℒ 2‐gain of switched systems with PDT is analyzed utilizing multiple QTD Lyapunov functions. Then, by constructing the quadratic discretized version of these functions, a synthesis condition for the discretized QTDℋ ∞controller is established. In order to formulate the synthesis condition in terms of LMIs, we employ the controller state reset strategy in the derivation, which means that the controller state is reset to that of the plant at each switching instant. Finally, a numerical example is given to illustrate the effectiveness of the proposed control scheme.