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Interval observers for linear functions of state vectors of linear fractional‐order systems with delayed input and delayed output
Author(s) -
Huong Dinh Cong
Publication year - 2019
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.2963
Subject(s) - observer (physics) , control theory (sociology) , mathematics , linear system , state (computer science) , interval (graph theory) , linear programming , constructive , state observer , upper and lower bounds , linear model , mathematical optimization , computer science , nonlinear system , algorithm , control (management) , mathematical analysis , process (computing) , physics , quantum mechanics , combinatorics , artificial intelligence , operating system , statistics
Summary This paper addresses the problem of interval observer design for linear functions of state vectors of linear fractional‐order systems, which are subjected to time delays in the measured output as well as the control input. By using the information of both the delayed output and input, we design two linear functional state observers to compute two estimates, an upper one and a lower one, which bound the unmeasured linear functions of state vectors. As a particular case with output delay only, we design a linear functional state observer to estimate (asymptotically) the unmeasured linear functions of state vectors. Existence conditions of such observers are provided, and some of them are translated into a linear programming problem, in which the observers' matrices can be effectively computed. Constructive design algorithms are introduced. Numerical examples are provided to illustrate the design procedure, practicality, and effectiveness of the proposed design method.