Stability of Time-Delay Systems

Gu, K.; Chen, Jie; Kharitonov, Vladimir L.

doi:10.1007/978-1-4612-0039-0

Cited by 4,040 publications

(2,408 citation statements)

References 214 publications

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“…Lemma 1. (Jensen's inequality) [33]: For any constant matrix S 4 0, scalars t 2 4 t 1 , vector function x : ½t 1 ; t 2 -R m such that the integrations in the following are well defined, then…”

Section: Stability Analysismentioning

confidence: 99%

Modified active disturbance rejection control for time-delay systems

2014

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Section: Stability Analysismentioning

confidence: 99%

Modified active disturbance rejection control for time-delay systems

2014

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“…Clearly the stability of the system (20) and (22) is the same as stability of the original system. Theorem 1: [24] Power model described in eq. (11) is asymptotically stable if there is an existence of a real symmetric matrix > 0 such that:…”

Section: Stability Analysis For Proposed Systemmentioning

confidence: 99%

Stability Analysis for Smart Homes Energy Management System with Delay Consideration

Umer¹,

Tan²,

Lim³

2014

JOCET

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Abstract-There is a tendency to consume electrical energy simultaneously by home appliances (HAs) leading to frequent demand peaks. Nowadays the number of (HAs) in modern residences has significantly increased as compared to the past. If the power demand is not met with the limited available power supply, this could lead to major power blackout. Our smart power management system consists of smart electric sensor (SES) and power provisioning controller (PPC). The PPC and SES are used to control and maintain stability with complete power waveform behavior examination. In this paper, we focus on achieving optimal system model for smart homes to reduce the risks of power blackout by applying two different criteria of power assignment for the HAs. A comparative study has been conducted which show the drastic change in the system behavior by changing the power assignment criteria. We also carry out the stability analysis for the proposed system model of smart homes. The stability analysis verifies that the system stability is dependent on some time delay. Simulation results also help us to observe critical system behaviors such as stability and overshoot of energy waveform.Index Terms-Power provisioning controller, smart electric sensor, maximum consuming power, home appliance power derivation, power supply/demand.

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“…By computingV (t) + 2αV (t) and by using some classic upper-bounds such as Jensen's inequality ( [6], Appendix B) and the convex approach from [19], we can show thaṫ…”

Section: B Main Stability Conditionsmentioning

confidence: 99%

Stability of piecewise affine systems with state-dependent delay, and application to congestion control

Fiter

Fridman

2013

52nd IEEE Conference on Decision and Control

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Abstract-In this work, we consider the exponential stability of piecewise affine systems with time-and state-dependent delay, and delayed-state-dependent switching. The stability analysis is based on the use of Lyapunov-Krasovskii functionals, and is divided into two parts. First, global stability conditions are proposed in the case of systems with (state-independent) time-varying delay. Then, local stability conditions are derived in the case of systems with time-and state-dependent delay. In the latter case, estimations of the domain of attraction are also proposed. The theoretical results are applied to the congestion control problem, which can be modelled by such systems.

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Stability of Time-Delay Systems

Cited by 4,040 publications

References 214 publications

Modified active disturbance rejection control for time-delay systems

Modified active disturbance rejection control for time-delay systems

Stability Analysis for Smart Homes Energy Management System with Delay Consideration

Stability of piecewise affine systems with state-dependent delay, and application to congestion control

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