Application of sample-data control for a class of time-delay nonlinear systems in circuit systems

Honghong Wang; Kai Wang; Honghong Wang; Kai Wang

doi:10.3934/math.2025514

AIMS Mathematics

2025, Volume 10, Issue 5: 11316-11329. doi: 10.3934/math.2025514

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Application of sample-data control for a class of time-delay nonlinear systems in circuit systems

Honghong Wang ,
Kai Wang ^,

College of Electrical Engineering, Qingdao University, Qingdao 266071, China

Received: 25 February 2025 Revised: 24 April 2025 Accepted: 06 May 2025 Published: 19 May 2025
MSC : 93C10, 94A17, 62B10

The problem of stability and stabilization for a class of circuit systems with time-varying delays via variable period sampled-data control was considered in this paper. First, the unique boundary conditions were utilized to handle the conic-type nonlinear terms. A Lyapunov-Krasovskii (L-K) functional, which can consider both time-varying delay and sampling time information, was constructed. Then, based on the free-weighting matrices and the improved reciprocally convex combination approach, sufficient conditions for system stabilization over a wider sampling interval were obtained in terms of Linear Matrix Inequalities (LMI), enabling the determination of controller gains. Finally, considering the impact of stable operation of the circuit system on the energy consumption and life cycle of the building, a time-delayed circuit system simulation verified our results, by assuming different upper bounds on time-delay and maximum sampling intervals and designing a modal-related sampled-data controller corresponding to them. The results showed the successful application of this method in the building circuit system, which provides theoretical support for the optimization of building energy consumption and the stable operation of the circuit system.
- Lyapunov-Krasovskii functional,
- sampled-data control,
- time-varying delay,
- stability,
- circuit system,
- building energy consumption and life cycle
Citation: Honghong Wang, Kai Wang. Application of sample-data control for a class of time-delay nonlinear systems in circuit systems[J]. AIMS Mathematics, 2025, 10(5): 11316-11329. doi: 10.3934/math.2025514

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Abstract

The problem of stability and stabilization for a class of circuit systems with time-varying delays via variable period sampled-data control was considered in this paper. First, the unique boundary conditions were utilized to handle the conic-type nonlinear terms. A Lyapunov-Krasovskii (L-K) functional, which can consider both time-varying delay and sampling time information, was constructed. Then, based on the free-weighting matrices and the improved reciprocally convex combination approach, sufficient conditions for system stabilization over a wider sampling interval were obtained in terms of Linear Matrix Inequalities (LMI), enabling the determination of controller gains. Finally, considering the impact of stable operation of the circuit system on the energy consumption and life cycle of the building, a time-delayed circuit system simulation verified our results, by assuming different upper bounds on time-delay and maximum sampling intervals and designing a modal-related sampled-data controller corresponding to them. The results showed the successful application of this method in the building circuit system, which provides theoretical support for the optimization of building energy consumption and the stable operation of the circuit system.

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