New asymptotic stability criteria for time-delayed dynamical systems with applications in control models

Arunagirinathan, S.; Muthukumar, P.

doi:10.1016/j.rico.2021.100014

Cited by 3 publications

(5 citation statements)

References 30 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Initialise b, AV, and CV in Equation (12) and Equation (13) Calculate the fitness of each search agent (i.e. XV α , XV β , and XV δ ) using Equation (27) Calculate θ:…”

Section: Randomly Initialise ωmentioning

confidence: 99%

“…In [11], LKF is employed with single-and double-integral terms for accurate integral inequalities and a new nonlinear optimisation technology was employed to solve the problem of nonlinear time-delay inequalities. In [12], LKF is employed with a triple integral term and using the method of integral inequality for one area and two area LFC. In [13], a modified LKF with delay-dependent matrices containing single-integral items and a unique negative definite inequality equivalent transformation lemma is utilised to translate the nonlinear inequality into LMIs for one and two-area LFC systems.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A Novel Computation of Delay Margin Based on Grey Wolf Optimisation for a Load Frequency Control of Two-Area-Network Power Systems

et al. 2023

View full text Add to dashboard Cite

In classical power systems, frequency measurements are transferred via a specialised communication channel, resulting in time delay. The time delay plays a major role in a power system, which can reduce the dynamic performance of the load–frequency control (LFC) system and can destabilise the system. The research to date has tended to focus on developing a new algorithm to determine the delay margin (DM) rather than looking into a hybrid algorithm which includes a nature-inspired metaheuristic optimisation technique. This paper introduces a novel method for computing the DM based on grey wolf optimisation (GWO), specifically for the constant time delay. In the proposed method, GWO is employed to optimise the minimum error of the spectral radius and to determine the best design variable of the crossing frequency. With the help of the proposed method, the sweeping range is no longer required, which improves the accuracy of the result. To evaluate the proposed method, a two-area network power system is considered as a case study. Furthermore, the effect of the PI controller gains on the DM is taken into account. The proposed method efficacy is demonstrated by comparing it with the most recently published methods. The results demonstrate that the proposed method is remarkably better than the existing methods found in the literature, where the smallest percentage inaccuracy using the simulation-based DM based on GWO is found to be 0.000%.

show abstract

“…Initialise b, AV, and CV in Equation (12) and Equation (13) Calculate the fitness of each search agent (i.e. XV α , XV β , and XV δ ) using Equation (27) Calculate θ:…”

Section: Randomly Initialise ωmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Novel Computation of Delay Margin Based on Grey Wolf Optimisation for a Load Frequency Control of Two-Area-Network Power Systems

et al. 2023

View full text Add to dashboard Cite

show abstract

“…Also, time delay leads to oscillation or instability of the control system in many cases. Therefore, a study on the stability of the dynamical model is attracted by many researchers [27], [28]. The major goal in the study of stability analysis for the control system with time delay is to expand the region of the feasibility for maximizing the upper delay bounds of the discussed control system, which also guarantees the system's stable performance with given constraints.…”

Section: ) Literature Reviewmentioning

confidence: 99%

“…To demonstrate the stability of the dynamical system, Lyapunov-Krasovskii functional (LKF) is one of the most working techniques, in which terms for stability analysis are derived in terms of linear matrix inequality (LMIs) [27].…”

Section: B Special Case Study: System Assessment Considering Time-var...mentioning

confidence: 99%

Adaptive LFC Incorporating Modified Virtual Rotor to Regulate Frequency and Tie-Line Power Flow in Multi-Area Microgrids

et al. 2022

View full text Add to dashboard Cite

This research investigates a new coordination strategy for both isolated single-area and interconnected multi-area microgrids (MGs) using a modified virtual rotor-based derivative technique supported with Jaya optimizer based on balloon effect modulation (BE). Accordingly, the main concept of BE is to assist the classic Jaya to be more sensitive and trackable in the event of disturbances, as well as to provide optimum integral gain value on the secondary frequency controller adaptively for both suggested MGs. The proposed modified virtual rotor mechanism is consisting of virtual inertia and virtual damping that are added as a tertiary controller within proposed MGs considering full participation of the inverter-based energy storage systems. The proposed virtual rotor mechanism is consisting of virtual inertia and virtual damping that are added as a tertiary controller within proposed MGs to emulate the reduction in system inertia and the enhanced damping properties. Several nonlinearities were proposed in this work such as a dead band of governor, generation rate constraints, and communication time-delay are considered within the dynamic model of the suggested MGs. In addition, the proposed design of multi-area MGs takes the interval timevarying communication delays into account for stability conditions. In this study, A comparative study using unimodal (i.e., Sphere) and multimodal (i.e., Rastrigin) benchmark test functions are conducted to validate the proposed direct adaptive Jaya-based BE. Furthermore, Wilcoxon's rank-signed non-parametric statistical test using a pairwise comparison was performed at a 5 % risk level to judge whether the proposed algorithm output varies from those of the other algorithms in a statistically significant manner. Thence, the superiority and effectiveness of the proposed method have also been verified against a variety of other metaheuristics optimization techniques, including classic electro-search, particle swarm, multi-objective seagull, and Jaya optimizers. In addition, an operative performance is assessed against the conventional integral controller, coefficient diagram method, and classic Jaya with/without virtual inertia. The final findings emphasize the superiority of the proposed direct adaptive Jaya-based BE supported by a modified virtual rotor and state better performance and stability compared to existing controllers.INDEX TERMS multi-area microgrids, virtual damping, virtual inertia, Jaya technique, adaptive control, balloon effect, coefficient diagram method, frequency regulation, time-varying delay.

show abstract

“…A new necessary and sufficient condition is proposed in [18], for the stability of any real matrix that does not need the information of the characteristic polynomial, and it is based on matrix entries' sign information only. Article [19] studies asymptotic stability criteria for time-delayed systems. Remarkable works have been done in [20,21] on matrices with stable sign patterns.…”

Section: Introductionmentioning

confidence: 99%

Qualitative sign stability of linear time invariant descriptor systems

2023

View full text Add to dashboard Cite

This article discusses assessing the instability of a continuous linear homogeneous timeinvariant descriptor system. Some necessary conditions and sufficient conditions are derived to establish the stability of a matrix pair by the fundamentals of qualitative ecological principles. The proposed conditions are derived using only the qualitative (sign) information of the matrix pair elements. Based on these conditions, the instability of a matrix pair can easily be determined, without any magnitude information of the matrix pair elements and without numerical eigenvalues calculations. With the proposed theory, Magnitude Dependent Stable, Magnitude Dependent Unstable, and Qualitative Sign Stable matrix pairs can be distinguished. The consequences of the proposed conditions and some illustrative examples are discussed.

show abstract

New asymptotic stability criteria for time-delayed dynamical systems with applications in control models

Cited by 3 publications

References 30 publications

A Novel Computation of Delay Margin Based on Grey Wolf Optimisation for a Load Frequency Control of Two-Area-Network Power Systems

A Novel Computation of Delay Margin Based on Grey Wolf Optimisation for a Load Frequency Control of Two-Area-Network Power Systems

Adaptive LFC Incorporating Modified Virtual Rotor to Regulate Frequency and Tie-Line Power Flow in Multi-Area Microgrids

Qualitative sign stability of linear time invariant descriptor systems

Contact Info

Product

Resources

About