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Robust stability analysis for linear systems with distributed delays: A time‐domain approach
Author(s) -
Juárez Luis,
Alexandrova Irina V.,
Mondié Sabine
Publication year - 2020
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.5244
Subject(s) - control theory (sociology) , stability (learning theory) , linear system , linear matrix inequality , computer science , simple (philosophy) , domain (mathematical analysis) , lyapunov function , mathematics , matrix (chemical analysis) , positive definite matrix , mathematical optimization , nonlinear system , control (management) , artificial intelligence , eigenvalues and eigenvectors , machine learning , materials science , epistemology , quantum mechanics , composite material , mathematical analysis , philosophy , physics
Summary This work is devoted to the robust stability analysis of linear systems with distributed delays. The approach is based on recent results in the Lyapunov‐Krasovskii framework, where a Lyapunov‐Krasovskii functional with prescribed negative definite derivative is applied. The stability conditions obtained in this work, are simple inequalities which depend on the so‐called delay Lyapunov matrix. The cases of matrix parameters and delays uncertainties are addressed, accurately detecting exact stability bounds when applied in an iterative manner. Our method is used successfully to tackle the challenging problem of robust predictor‐based stabilization of systems with state and input delays.