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

Hongli Yang, Chengdan Wang, Xiao Bi and Ivan Ganchev Ivanov ()
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Hongli Yang: College of Big Data, Qingdao Huanghai University, Linghai Road 1145, Qingdao 266427, China
Chengdan Wang: College of Mathematics and Systems Science, Shandong University of Science and Technology, Qianwangang Road 579, Qingdao 266590, China
Xiao Bi: School of Mathematics, Shandong University, Jinan 250100, China
Ivan Ganchev Ivanov: Faculty of Economics and Business Administration, Sofia University “St. Kl. Ohridski”, 1000 Sofia, Bulgaria

Mathematics, 2024, vol. 12, issue 16, 1-14

Abstract: 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.

Keywords: robust invariant set; uncertain discrete-time systems; duality; semidefinite programming (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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