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Pseudo‐predictor feedback control of discrete‐time linear systems with a single input delay
Author(s) -
Zhou Bin,
Yang Xuefei,
Lam James
Publication year - 2015
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.3478
Subject(s) - control theory (sociology) , stability (learning theory) , controller (irrigation) , state (computer science) , feedback control , actuator , class (philosophy) , linear system , computer science , discrete time and continuous time , mathematics , control (management) , control engineering , engineering , algorithm , mathematical analysis , statistics , machine learning , agronomy , artificial intelligence , biology
Summary This paper studies the problems of stabilization of discrete‐time linear systems with a single input delay. By developing the methodology of pseudo‐predictor feedback, which uses the (artificial) closed‐loop system dynamics to predict the future state, memoryless state feedback control laws are constructed to solve the problem. Necessary and sufficient conditions are obtained to guarantee the stability of the closed‐loop system in terms of the stability of a class‐difference equations. It is also shown that the proposed controller achieves semi‐global stabilization of the system if its actuator is subject to either magnitude saturation or energy constraints under the condition that the open‐loop system is only polynomially unstable. Numerical examples have been worked out to illustrate the effectiveness of the proposed approaches. Copyright © 2015 John Wiley & Sons, Ltd.