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Relaxed results on reachable set estimation of time‐delay systems with bounded peak inputs
Author(s) -
Zhang Baoyong,
Lam James,
Xu Shengyuan
Publication year - 2016
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.3395
Subject(s) - bounded function , ellipsoid , mathematics , differentiable function , regular polygon , positive definite matrix , scalar (mathematics) , linear matrix inequality , lyapunov function , control theory (sociology) , nonlinear system , mathematical optimization , mathematical analysis , computer science , control (management) , physics , geometry , quantum mechanics , astronomy , artificial intelligence , eigenvalues and eigenvectors
Summary This paper is concerned with the problem of reachable set estimation (RSE) for linear systems with time‐varying delays and bounded peak inputs. The purpose is to find an ellipsoid that contains the system state in presence of all bounded peak inputs. First, the RSE problem for nominal time‐delay systems is studied based on a relaxed Lyapunov–Krasovskii functional which does not require all the involved symmetric matrices to be positive definite. Delay‐dependent and delay‐rate‐dependent conditions for the existence of a desired ellipsoid are obtained. Second, the RSE problem for time‐delay systems with time‐varying polytopic uncertainties is investigated. Under the assumption that the uncertain parameters are differentiable and their derivatives are bounded by known scalars, parameter‐rate‐dependent conditions for the existence of a desired ellipsoid are derived by using a parameter‐dependent Lyapunov–Krasovskii functional. When the differentiability of the uncertain parameters is not taken into account, a common Lyapunov–Krasovskii functional is employed to tackle the addressed problem, and parameter‐rate‐independent conditions are presented. All the obtained conditions are given in terms of matrix inequalities, which become linear matrix inequalities when only one non‐convex scalar is prescribed. Finally, the reduced conservatism of the obtained results in comparison with recent ones in the literature is shown through numerical examples. Copyright © 2015 John Wiley & Sons, Ltd.