Aperiodic intermittent control for discrete-time systems

Huijuan Li; Yanbin Ning; Huijuan Li; Yanbin Ning

doi:10.3934/math.2025867

AIMS Mathematics

2025, Volume 10, Issue 8: 19412-19437. doi: 10.3934/math.2025867

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Research article

Aperiodic intermittent control for discrete-time systems

Huijuan Li ^{1
,
,},
Yanbin Ning ²

1.
School of Mathematics and Physics, China University of Geosciences(Wuhan), 430074, Wuhan, China
2.
Research department, Shandong Shijiu Communication Technology Co.,LTD, Xingfu, 250000, Shandong, China

Received: 06 June 2025 Revised: 07 August 2025 Accepted: 13 August 2025 Published: 26 August 2025
MSC : 93C10, 93C55, 93C95, 93C57, 34H15, 34E05

In this manuscript, time-triggered and event-triggered aperiodic intermittent controls are proposed for asymptotic stabilization of unstable discrete-time systems. The time-triggered aperiodic intermittent controls (T-APICs) are designed respectively by imposing conditions on the average dwell-time and the minimum of the active control width. For event-triggered aperiodic intermittent controls (E-APICs), when the norm of the state violates the defined inequality, the control is triggered. For one proposed E-APIC mechanism, it is demanded that the control length should be bigger than a given constant. Then for another E-APIC mechanism, we impose a condition related to the state on the control length. By relaxing the constraints on the control gain matrix, the third E-APIC mechanism is proposed. For these control plans, the control continuously updates during the active control time interval. Then we propose another E-APIC for asymptotic stabilization of the discussed discrete-time system by using the concept of input -to-state stability (ISS) and imposing the conditions on the norm of the state. In order to exemplify the effectiveness of the proposed aperiodic intermittent control mechanisms, asymptotic stabilizations of three examples are discussed by the proposed theorems.
Citation: Huijuan Li, Yanbin Ning. Aperiodic intermittent control for discrete-time systems[J]. AIMS Mathematics, 2025, 10(8): 19412-19437. doi: 10.3934/math.2025867

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Abstract

In this manuscript, time-triggered and event-triggered aperiodic intermittent controls are proposed for asymptotic stabilization of unstable discrete-time systems. The time-triggered aperiodic intermittent controls (T-APICs) are designed respectively by imposing conditions on the average dwell-time and the minimum of the active control width. For event-triggered aperiodic intermittent controls (E-APICs), when the norm of the state violates the defined inequality, the control is triggered. For one proposed E-APIC mechanism, it is demanded that the control length should be bigger than a given constant. Then for another E-APIC mechanism, we impose a condition related to the state on the control length. By relaxing the constraints on the control gain matrix, the third E-APIC mechanism is proposed. For these control plans, the control continuously updates during the active control time interval. Then we propose another E-APIC for asymptotic stabilization of the discussed discrete-time system by using the concept of input -to-state stability (ISS) and imposing the conditions on the norm of the state. In order to exemplify the effectiveness of the proposed aperiodic intermittent control mechanisms, asymptotic stabilizations of three examples are discussed by the proposed theorems.

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