Functional observer design for retarded system with interval time-varying delays

Document Type

Article

Publication Date

4-4-2017

Publication Title

International Journal of Systems Science

Volume

48

Issue

5

First Page

1060

Keywords

Functional observers, interval time delay, linear matrix inequality, Lyapunov–Krasovskii functional, Wirtinger-based inequality

Last Page

1070

Abstract

Functional observers are the key solution to numerous practical estimation problems, wherein full-order observers cannot be applied. This paper studies the novel problem of minimum-order functional observer design for time-delay systems with interval time-varying state delays. Moreover, unlike the majority of the existing papers on this topic, which consider either small or unknown delay rates, the delay derivative is assumed to possess an upper bound not limited to be less than one. A new augmented Lyapunov–Krasovskii functional with triple integral terms is employed to derive less conservative delay-dependent sufficient conditions for the stability of the closed-loop observer dynamics, which are expressed in terms of linear matrix inequalities. In addition, contemporary techniques such as Wirtinger-based single- and double-integral inequalities, delay splitting scheme, reciprocally convex approach and convex combination technique, along with the descriptor transformation, are adopted in constructing the new stability criterion that is exploited for obtaining the observer parameters. A genetic-algorithm-based searching schema is proposed to optimally tune a number of weighting parameters in the observer design procedure. Numerical examples and simulation results are demonstrated to confirm the effectiveness and the superiority of the proposed observer design algorithm.

DOI

10.1080/00207721.2016.1236422

ISSN

00207721

E-ISSN

14645319

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