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Stability of a Trajectory‐Based Control Law for an Unknown Nonlinear Non‐Minimum Phase System
Author(s) -
Brockwell Anthony,
Evans Rob,
Mareels Iven
Publication year - 2001
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 - 10.1111/j.1934-6093.2001.tb00041.x
Subject(s) - trajectory , control theory (sociology) , nonlinear system , interval (graph theory) , mathematics , stability (learning theory) , sampling (signal processing) , minimum phase , discrete time and continuous time , phase (matter) , law , control (management) , computer science , physics , statistics , filter (signal processing) , quantum mechanics , astronomy , artificial intelligence , combinatorics , machine learning , political science , computer vision
We investigate the stability of an unknown nonlinear discrete‐time non‐minimum phase system under a trajectory‐based control law. The system can be regarded as a first‐order approximation to a continuous‐time system. Hence, one of the parameters in the discrete‐time system equation can be regarded as the “sampling interval”. We show that, subject to certain conditions, as long as the sampling interval is neither too short nor too long, the closed‐loop system is stable in a certain sense.