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Observer‐Based Reliable Control for Discrete‐Time Switched Linear Systems with Faulty Actuators
Author(s) -
Li Jiao,
Zhao Jun
Publication year - 2012
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1002/asjc.474
Subject(s) - control theory (sociology) , observer (physics) , actuator , linear matrix inequality , controller (irrigation) , state (computer science) , stability (learning theory) , discrete time and continuous time , mathematics , matrix (chemical analysis) , state observer , computer science , control (management) , linear system , mathematical optimization , algorithm , nonlinear system , mathematical analysis , statistics , physics , materials science , quantum mechanics , artificial intelligence , machine learning , agronomy , composite material , biology
This paper deals with the issue of reliable control for discrete‐time switched linear systems with faulty actuators by utilizing a multiple L yapunov functions method and estimate state‐dependent switching technique. A solvability condition for the reliable control problem is given in terms of matrix inequality with an extra matrix variable. This condition allows the reliable control problem for each individual subsystem to be unsolvable. For each subsystem of such a switched system, we design an observer and an observer‐based controller. A switching rule depending on the observer state is designed which, together with the controllers, can guarantee the stability of the closed‐loop switched system for all admissible actuator failures. The observers, controllers, and switching law are explicitly computed by solving linear matrix inequalities ( LMIs ). The proposed design method is illustrated by two numerical examples.