New delay-range-dependent exponential stability criterion and $ H_\infty $ performance for neutral-type nonlinear system with mixed time-varying delays

Boonyachat Meesuptong; Peerapongpat Singkibud; Pantiwa Srisilp; Kanit Mukdasai; Boonyachat Meesuptong; Peerapongpat Singkibud; Pantiwa Srisilp; Kanit Mukdasai

doi:10.3934/math.2023033

AIMS Mathematics

2023, Volume 8, Issue 1: 691-712. doi: 10.3934/math.2023033

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Research article

New delay-range-dependent exponential stability criterion and $ H_\infty $ performance for neutral-type nonlinear system with mixed time-varying delays

1.
Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand
2.
Department of Applied Mathematics and Statistics, Faculty of Science and Liberal Arts, Rajamangala University of Technology Isan, Nakhon Ratchasima 30000, Thailand
3.
Rail System Institute of Rajamangala University of Technology Isan, Nakhon Ratchasima 30000, Thailand

Received: 19 July 2022 Revised: 21 September 2022 Accepted: 26 September 2022 Published: 11 October 2022
MSC : 93B36, 93C43, 93D23

For a neutral system with mixed discrete, neutral and distributed interval time-varying delays and nonlinear uncertainties, the problem of exponential stability is investigated in this paper based on the $ H_\infty $ performance condition. The uncertainties are nonlinear time-varying parameter perturbations. By introducing a decomposition matrix technique, using Jensen's integral inequality, Peng-Park's integral inequality, Leibniz-Newton formula and Wirtinger-based integral inequality, utilization of a zero equation and the appropriate Lyapunov-Krasovskii functional, new delay-range-dependent sufficient conditions for the $ H_\infty $ performance with exponential stability of the system are presented in terms of linear matrix inequalities. Moreover, we present numerical examples that demonstrate exponential stability of the neutral system with mixed time-varying delays, and nonlinear uncertainties to show the advantages of our method.
- exponential stability,
- $ H_\infty $ performance,
- neutral system,
- time-varying delay
Citation: Boonyachat Meesuptong, Peerapongpat Singkibud, Pantiwa Srisilp, Kanit Mukdasai. New delay-range-dependent exponential stability criterion and $ H_\infty $ performance for neutral-type nonlinear system with mixed time-varying delays[J]. AIMS Mathematics, 2023, 8(1): 691-712. doi: 10.3934/math.2023033

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Abstract

For a neutral system with mixed discrete, neutral and distributed interval time-varying delays and nonlinear uncertainties, the problem of exponential stability is investigated in this paper based on the $ H_\infty $ performance condition. The uncertainties are nonlinear time-varying parameter perturbations. By introducing a decomposition matrix technique, using Jensen's integral inequality, Peng-Park's integral inequality, Leibniz-Newton formula and Wirtinger-based integral inequality, utilization of a zero equation and the appropriate Lyapunov-Krasovskii functional, new delay-range-dependent sufficient conditions for the $ H_\infty $ performance with exponential stability of the system are presented in terms of linear matrix inequalities. Moreover, we present numerical examples that demonstrate exponential stability of the neutral system with mixed time-varying delays, and nonlinear uncertainties to show the advantages of our method.

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