Paper Info
Title
Robust Stability Conditions For A Family Of Linear Discrete-Time Systems Subjected To Uncertainties
Abstract
Robust stability conditions are established for a family of linear discrete-time systems subjected to uncertainties. The traditional approach, which involves the construction of a common quadratic Lyapunov function for the entire family of systems with uncertainty, often leads to the problem of conservatism. In this connection, constructing parametric quadratic Lyapunov functions seems promising. The main tools of the proposed approach are the apparatus of linear matrix inequalities and a modification, presented here, of the well-known Petersen's lemma. A simple approach to finding the robust quadratic stability radius of the family in question is proposed in the paper as well. The corresponding optimization problems have the form of semidefinite programming and one-dimensional minimization, which can be easily solved numerically. The efficiency of our approach is demonstrated via a numerical example. The results obtained can be generalized to design problems for linear discrete-time systems subjected to uncertainties, to other robust statements, and to the case of exogenous disturbances.
Year
DOI
Venue
2021
10.1134/S0005117921080117
AUTOMATION AND REMOTE CONTROL
Keywords
DocType
Volume
linear discrete-time system, parametric Lyapunov function, structured matrix uncertainty, robustness, linear matrix inequality
Journal
82
Issue
ISSN
Citations 
8
0005-1179
0
PageRank 
References 
Authors
0.34
0
2
Name
Order
Citations
PageRank
Mikhail V. Khlebnikov121.54
Yana I. Kvinto200.34