Stability analysis of linear systems with time‐varying delay via a quadratic function negative‐definiteness determination method | Zendy

Long Fei | Zendy; Lin WenJuan | Zendy; He Yong | Zendy; Jiang Lin | Zendy; Wu Min | Zendy

Open Access

Stability analysis of linear systems with time‐varying delay via a quadratic function negative‐definiteness determination method

Author(s) -

Long Fei,

Lin WenJuan,

He Yong,

Jiang Lin,

Wu Min

Publication year - 2020

Publication title -

iet control theory and applications

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.059

H-Index - 108

eISSN - 1751-8652

pISSN - 1751-8644

DOI - 10.1049/iet-cta.2019.0471

Subject(s) - control theory (sociology) , definiteness , quadratic equation , stability (learning theory) , positive definiteness , linear control systems , mathematics , function (biology) , quadratic function , linear system , positive definite matrix , computer science , mathematical analysis , control (management) , physics , artificial intelligence , eigenvalues and eigenvectors , philosophy , linguistics , geometry , quantum mechanics , machine learning , evolutionary biology , biology

This study aims to carry out the stability analysis of linear systems with a time‐varying delay. It is known that the negative‐definite condition of the derivative of a Lyapunov–Krasovskii functional (LKF) can be determined using the convex combination method if the convexity requirement is satisfied by the derivative of the LKF. However, this method is not feasible in cases where the LKF's derivative is a quadratic function. To address this problem, this study proposes a novel negative‐definiteness determination lemma that encompasses the previous lemmas as its special cases and shows less conservatism. Then, this lemma is employed to derive a stability criterion, and its superiority is demonstrated using three examples.

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