Robust stabilization for uncertain saturated systems with multiple time delays

Yuzhen Chen; Haoxin Liu; Rui Dong; Yuzhen Chen; Haoxin Liu; Rui Dong

doi:10.3934/math.20221053

AIMS Mathematics

2022, Volume 7, Issue 10: 19180-19201. doi: 10.3934/math.20221053

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Research article

Robust stabilization for uncertain saturated systems with multiple time delays

School of Mathematical Sciences, Henan Institute of Science and Technology, Xinxiang 453003, China

Received: 20 May 2022 Revised: 11 August 2022 Accepted: 15 August 2022 Published: 30 August 2022
MSC : 93D09

This paper is concerned with the robust stabilization problem for uncertain saturated linear systems with multiple discrete delays. First of all, a new distributed-delay-dependent polytopic approach is proposed, and a new type of Lyapunov-Krasovskii functional is constructed. Then, by further incorporating some integral inequalities, both stabilization and robust stabilization conditions are proposed in terms of linear matrix inequalities under which the closed-loop systems are asymptotically stable for admissible initial conditions. Finally, a simulation example is given to illustrate the feasibility and advantages of the obtained results.
- regional stabilization,
- uncertain systems,
- multiple delays,
- actuator saturation,
- polytopic approach
Citation: Yuzhen Chen, Haoxin Liu, Rui Dong. Robust stabilization for uncertain saturated systems with multiple time delays[J]. AIMS Mathematics, 2022, 7(10): 19180-19201. doi: 10.3934/math.20221053

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Abstract

This paper is concerned with the robust stabilization problem for uncertain saturated linear systems with multiple discrete delays. First of all, a new distributed-delay-dependent polytopic approach is proposed, and a new type of Lyapunov-Krasovskii functional is constructed. Then, by further incorporating some integral inequalities, both stabilization and robust stabilization conditions are proposed in terms of linear matrix inequalities under which the closed-loop systems are asymptotically stable for admissible initial conditions. Finally, a simulation example is given to illustrate the feasibility and advantages of the obtained results.

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