Hierarchical stability conditions for aperiodic sampled-data control systems with fixed delay

Xiao-Gui Liu; Feng-Ling Jiang; Wen-Kai Wang; Xin Zhou; Xiao-Gui Liu; Feng-Ling Jiang; Wen-Kai Wang; Xin Zhou

doi:10.3934/era.2026150

Electronic Research Archive

2026, Volume 34, Issue 5: 3334-3349. doi: 10.3934/era.2026150

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Research article

Hierarchical stability conditions for aperiodic sampled-data control systems with fixed delay

1.
School of Railway Power Supply and Electrical Engineering, Hunan Railway Professional Technology College, Zhuzhou 412001, China
2.
Hunan High Speed Railway Operation Safety Assurance Engineering Technology Research Center, Zhuzhou 412006, China
3.
College of Science, Hunan University of Technology, Zhuzhou 412007, China

Received: 26 November 2025 Revised: 26 February 2026 Accepted: 05 March 2026 Published: 17 April 2026

This paper deals with the stability issue of aperiodic sampled-data control systems with fixed delay. First, to obtain the less conservative stability criterion, the hierarchical looped-functional is assembled. In the functional, the integrals in the integral inequalities are directly utilized in the construction. Hence, the integrals of the system equation are prevented to avoid the products of the free matrices and system matrices. Also, the integrals over the segmented interval $ [t, t-\gamma] $ are introduced. Then, by employing the generalized free-matrix-based integral inequalities, the integrals of the same quadratic product term over different time intervals are estimated to acquire the linear functions of these intervals. Next, the hierarchical stability conditions are presented in terms of the linear matrix inequalities based on the Schur complement. Finally, some numeric examples are used to illustrate the superiority of the proposed method.
- aperiodic sampled-data control systems,
- hierarchical looped functional,
- stability,
- generalized free-matrix-based integral inequalities
Citation: Xiao-Gui Liu, Feng-Ling Jiang, Wen-Kai Wang, Xin Zhou. Hierarchical stability conditions for aperiodic sampled-data control systems with fixed delay[J]. Electronic Research Archive, 2026, 34(5): 3334-3349. doi: 10.3934/era.2026150

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Abstract

This paper deals with the stability issue of aperiodic sampled-data control systems with fixed delay. First, to obtain the less conservative stability criterion, the hierarchical looped-functional is assembled. In the functional, the integrals in the integral inequalities are directly utilized in the construction. Hence, the integrals of the system equation are prevented to avoid the products of the free matrices and system matrices. Also, the integrals over the segmented interval $ [t, t-\gamma] $ are introduced. Then, by employing the generalized free-matrix-based integral inequalities, the integrals of the same quadratic product term over different time intervals are estimated to acquire the linear functions of these intervals. Next, the hierarchical stability conditions are presented in terms of the linear matrix inequalities based on the Schur complement. Finally, some numeric examples are used to illustrate the superiority of the proposed method.

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