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Mixed H ∞ and passive filtering for linear switched systems with average dwell time
Author(s) -
Zheng Qunxian,
Guo Xingzhong,
Zhang Hongbin
Publication year - 2018
Publication title -
international journal of adaptive control and signal processing
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.73
H-Index - 66
eISSN - 1099-1115
pISSN - 0890-6327
DOI - 10.1002/acs.2844
Subject(s) - passivity , control theory (sociology) , dwell time , lyapunov function , mathematics , observer (physics) , set (abstract data type) , linear system , filtering problem , computer science , filter (signal processing) , control (management) , filter design , nonlinear system , engineering , artificial intelligence , clinical psychology , mathematical analysis , physics , quantum mechanics , electrical engineering , computer vision , programming language , medicine
Summary In this paper, a new performance index is proposed for switched systems. The new performance index can be viewed as the mixed weighted H ∞ and passivity performance. This new performance index covers the weighted H ∞ performance and the passivity performance as special cases. Based on this new performance index, the weighted H ∞ filtering problem and the passive filtering problem of linear switched systems with unstable subsystems are solved in a unified framework. The states of the filtering error system constructed by the augmentation technique will be divergent when unstable subsystems are activated. To overcome this problem, a set of mode‐dependent filters of a Luenberger‐like observer type is constructed. The multiple Lyapunov function approach and the average dwell‐time technique are employed to solve the mixed filtering problem. New sufficient conditions for the existence of mixed H ∞ and passive filters are developed, which ensure the filtering error system to be asymptotically stable with a prescribed mixed H ∞ and passivity performance index. Moreover, the desired mixed H ∞ and passive filters can be constructed by solving a set of linear matrix inequalities. Finally, numerical examples are given to demonstrate the applicability and advantage of the obtained results.