Robust Invariance Conditions of Uncertain Linear Discrete Time Systems Based on Semidefinite Programming Duality

This article proposes a novel robust invariance condition for uncertain linear discrete-time systems with state and control constraints, utilizing a method of semidefinite programming duality. The approach involves approximating the robust invariant set for these systems by tackling the dual problem...

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Bibliographic Details
Published in:Mathematics (Basel) Vol. 12; no. 16; p. 2512
Main Authors: Yang, Hongli, Wang, Chengdan, Bi, Xiao, Ivanov, Ivan Ganchev
Format: Journal Article
Language:English
Published: Basel MDPI AG 01.08.2024
Subjects:
Algorithms
Approximation
Discrete time systems
duality
Dynamical systems
Invariance
Linear matrix inequalities
Linear programming
Optimization
Programming
Robust control
robust invariant set
Semidefinite programming
uncertain discrete-time systems
ISSN:2227-7390, 2227-7390
Online Access:Get full text
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Summary:This article proposes a novel robust invariance condition for uncertain linear discrete-time systems with state and control constraints, utilizing a method of semidefinite programming duality. The approach involves approximating the robust invariant set for these systems by tackling the dual problem associated with semidefinite programming. Central to this method is the formulation of a dual programming through the application of adjoint mapping. From the standpoint of semidefinite programming dual optimization, the paper presents a novel linear matrix inequality (LMI) conditions pertinent to robust positive invariance. Illustrative examples are incorporated to elucidate the findings.
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ISSN:2227-7390
2227-7390
DOI:10.3390/math12162512