An improved reachable set estimation for time-delay linear systems with peak-bounded inputs and polytopic uncertainties via augmented zero equality approach

Yonggwon Lee; Yeongjae Kim; Seunghoon Lee; Junmin Park; Ohmin Kwon; Yonggwon Lee; Yeongjae Kim; Seunghoon Lee; Junmin Park; Ohmin Kwon

doi:10.3934/math.2023293

AIMS Mathematics

2023, Volume 8, Issue 3: 5816-5837. doi: 10.3934/math.2023293

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Research article

An improved reachable set estimation for time-delay linear systems with peak-bounded inputs and polytopic uncertainties via augmented zero equality approach

1.
School of Electrical Engineering, Chungbuk National University, Cheongju 28644, Republic of Korea
2.
Department of Electronics Engineering, Chungnam National University, Daejeon 34134, Republic of Korea

Received: 13 October 2022 Revised: 05 December 2022 Accepted: 06 December 2022 Published: 26 December 2022
MSC : 34D20, 34K20, 34K25

This paper proposes an improved estimation of the reachable set (RS) analysis in linear systems with polytopic uncertainties, peak-bounded inputs and time-varying delay. Inspired by past literature, Lyapunov-Krasovskii's functionals are dealt for treating the time-delay and bounding analysis effectively. So, the proposed method focuses on Lyapunov-Krasovskii's functionals via various time-delay conditions for linear systems. Based on the Lyapunov method, some integral inequalities, useful zero equalities, and the augmented zero equality approach are introduced. The results are expressed in terms of linear matrix inequalities, which are easy to get optimized solutions for obtaining guaranteed minimum RS of system dynamics. Finally, two numerical examples are shown to judge that the proposed estimation method can lead to less conservative results.
- reachable set,
- time delay systems,
- peak-input,
- linear systems,
- Lyapunov method
Citation: Yonggwon Lee, Yeongjae Kim, Seunghoon Lee, Junmin Park, Ohmin Kwon. An improved reachable set estimation for time-delay linear systems with peak-bounded inputs and polytopic uncertainties via augmented zero equality approach[J]. AIMS Mathematics, 2023, 8(3): 5816-5837. doi: 10.3934/math.2023293

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Abstract

This paper proposes an improved estimation of the reachable set (RS) analysis in linear systems with polytopic uncertainties, peak-bounded inputs and time-varying delay. Inspired by past literature, Lyapunov-Krasovskii's functionals are dealt for treating the time-delay and bounding analysis effectively. So, the proposed method focuses on Lyapunov-Krasovskii's functionals via various time-delay conditions for linear systems. Based on the Lyapunov method, some integral inequalities, useful zero equalities, and the augmented zero equality approach are introduced. The results are expressed in terms of linear matrix inequalities, which are easy to get optimized solutions for obtaining guaranteed minimum RS of system dynamics. Finally, two numerical examples are shown to judge that the proposed estimation method can lead to less conservative results.

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