Novel stability criterion for linear system with two additive time-varying delays using general integral inequalities

Yude Ji; Xitong Ma; Luyao Wang; Yanqing Xing; Yude Ji; Xitong Ma; Luyao Wang; Yanqing Xing

doi:10.3934/math.2021504

AIMS Mathematics

2021, Volume 6, Issue 8: 8667-8680. doi: 10.3934/math.2021504

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Research article

Novel stability criterion for linear system with two additive time-varying delays using general integral inequalities

School of Sciences, Hebei University of Science and Technology, Shijiazhuang, 050018, Hebei, China

Received: 14 March 2021 Accepted: 27 May 2021 Published: 07 June 2021
MSC : 34D20, 34K20, 93D05

The stability analysis strategy for continuous linear system with two additive time-varying delays is proposed in this paper. First, for the purpose of analysis, the novel Lyapunov-Krasovskii functional (LKF) consisting of integral terms based on the first-order derivative of the system state is constructed. Second, the derivative of LKF is estimated by utilizing the Wirtinger-based integral inequality and extended reciprocally convex matrix inequality. The delay-dependent stability criterions are established in terms of linear matrix inequalities (LMIs) framework. The results show that the system performances are improved based on both enlarging the maximum allowable upper bound of the time-delays and reducing the number of decision variables. Furthermore, the conservatism of obtained delay-dependent stability criterion is reduced. Finally, a numerical simulation is given to demonstrate the effectiveness of obtained theoretical results.
- linear system,
- time-varying delays,
- stability,
- Lyapunov-Krasovskii functional (LKF),
- linear matrix inequalities (LMIs)
Citation: Yude Ji, Xitong Ma, Luyao Wang, Yanqing Xing. Novel stability criterion for linear system with two additive time-varying delays using general integral inequalities[J]. AIMS Mathematics, 2021, 6(8): 8667-8680. doi: 10.3934/math.2021504

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Abstract

The stability analysis strategy for continuous linear system with two additive time-varying delays is proposed in this paper. First, for the purpose of analysis, the novel Lyapunov-Krasovskii functional (LKF) consisting of integral terms based on the first-order derivative of the system state is constructed. Second, the derivative of LKF is estimated by utilizing the Wirtinger-based integral inequality and extended reciprocally convex matrix inequality. The delay-dependent stability criterions are established in terms of linear matrix inequalities (LMIs) framework. The results show that the system performances are improved based on both enlarging the maximum allowable upper bound of the time-delays and reducing the number of decision variables. Furthermore, the conservatism of obtained delay-dependent stability criterion is reduced. Finally, a numerical simulation is given to demonstrate the effectiveness of obtained theoretical results.

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