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Reliable H ∞ control for 2‐D discrete switched systems with state delays and actuator failures
Author(s) -
Badie Khalid,
Alfidi Mohammed,
Chalh Zakaria
Publication year - 2020
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.3156
Subject(s) - control theory (sociology) , actuator , dwell time , exponential stability , state (computer science) , controller (irrigation) , state space , stability (learning theory) , mathematics , computer science , exponential function , control (management) , algorithm , mathematical analysis , physics , statistics , artificial intelligence , clinical psychology , nonlinear system , quantum mechanics , machine learning , agronomy , biology , medicine
Summary This article is concerned with the reliable H ∞ control problem against actuator failures for discrete two‐dimensional (2‐D) switched systems with state delays and actuator faults described by the second Fornasini‐Marchesini (FM) state‐space model. By resorting to the average dwell time (ADT) approach, also by constructing an appropriate Lyapunov‐Krasovskii functional and using the Wirtinger inequality, some sufficient conditions for the exponential stability analysis and weighted H ∞ performance of the given system are derived. Then, based on the obtained conditions, a reliable H ∞ controller design approach is presented such that the resulting closed‐loop system is exponentially stable with a weighted H ∞ performance γ , not only when all actuators are in normal conditions, but also in the case of some actuator failures. Finally, two numerical examples are examined to demonstrate the effectiveness of the proposed results.