Improved Delay-Dependent Stability Analysis of Fixed-Point State-Space Digital Filters With Time-Varying Delay and Generalized Overflow Arithmetic

Li, Fudong, Chen, Jian, Zhang, Lanhong, Wang, Qibing and Jiang, Lin ORCID: 0000-0001-6531-2791 (2022) Improved Delay-Dependent Stability Analysis of Fixed-Point State-Space Digital Filters With Time-Varying Delay and Generalized Overflow Arithmetic IEEE Access, 10. pp. 9406-9419. ISSN 2169-3536, 2169-3536

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Abstract

This paper is concerned with the stability analysis of fixed-point state-space digital filters with generalized overflow arithmetic and a time-varying delay. This paper aims to derive a delay and nonlinear function bound dependent asymptotical stability criterion with less conservatism. Firstly, a new Lyapunov functional with several augmented terms, including extra free matrices and overflow nonlinear function, is constructed such that it has a relaxed positive condition. Then, for bounding the summation term arising in the forward difference of Lyapunov functional, a new lemma is developed to introduce the terms for linking the delayed states and the overflow nonlinear function, the Wirtinger-based summation inequality and several zero-value terms are applied to add more cross terms. As a result, a stability criterion with less conservatism is established and its conservatism. Finally, several numerical examples are given to illustrate the advantages of the proposed method.

Item Type:	Article
Uncontrolled Keywords:	Delays, Stability criteria, Numerical stability, Linear matrix inequalities, Asymptotic stability, Arithmetic, Symmetric matrices, digital filter, generalized overflow arithmetic, time-varying delay
Divisions:	Faculty of Science & Engineering > School of Electrical Engineering, Electronics and Computer Science
Depositing User:	Symplectic Admin
Date Deposited:	08 Feb 2022 11:44
Last Modified:	01 Mar 2026 03:10
DOI:	10.1109/access.2022.3143309
Open Access URL:	https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&ar...
Related Websites:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3148495
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