Open AccessRobust H ∞ control for a class of non‐linear discrete time‐delay systems with controller failure: a probability‐dependent method
Author(s) -
Nie Hong,
Sang Hong,
Li Ping
Publication year - 2017
Publication title -
iet control theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.059
H-Index - 108
eISSN - 1751-8652
pISSN - 1751-8644
DOI - 10.1049/iet-cta.2017.0703
Subject(s) - dwell time , control theory (sociology) , controller (irrigation) , probabilistic logic , piecewise , discrete time and continuous time , computer science , lyapunov function , probability density function , piecewise linear function , mathematics , control (management) , nonlinear system , artificial intelligence , statistics , medicine , clinical psychology , mathematical analysis , physics , geometry , quantum mechanics , agronomy , biology
This study addresses the issue of robust H ∞ control for a class of discrete‐time delayed non‐linear systems in the presence of controller failure by using a probability‐dependent method. Considering the stochasticity and inevitability of controller failure, they propose a notion of controller probabilistic failure. Based on the idea of switching, the studied systems are converted into a kind of stochastic switched systems. When the probability information is available, a probability‐dependent switching strategy is developed by application of piecewise Lyapunov function and average dwell time approaches such that the system is exponentially mean square stable with weighted H ∞ performance. At the same time, a probability‐dependent weighted H ∞ switching controller is designed. Moreover, the obtained results are also shown to be feasible when the probability information cannot be known accurately. Finally, two simulation examples are provided to illustrate the effectiveness of the proposed method.