Routh-Hurwitz Criterion for Stability: An Overview and Its Implementation on Characteristic Equation Vectors Using MATLAB

Patil, Aseem

doi:10.1007/978-981-15-9927-9_32

Cited by 10 publications

(5 citation statements)

References 3 publications

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“…2 + i ω m1 and M 2 = κ b2 2 + i ω m2 . Now, the Routh array can be written as, After numerically solving the characteristic equation we find that all the coefficients in the first column of the Routh array [84,85] have the same sign and are non-zero. Therefore, we conclude that our system is stable.…”

Section: Discussionmentioning

confidence: 99%

Coupling of QD-based PhC nanocavity with two mechanical modes: an approach to tunable optical switching and sensing applications

Yeasmin

Barbhuiya

Bhattacherjee

et al. 2023

J. Opt.

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We theoretically study the dynamical change in the ampliﬁcation of the output probe ﬁeld spectra of a hybrid optomechanical system consisting of two mechanical modes coupled to a photonic crystal (PhC) nanocavity. The PhC cavity is also embedded with a quantum dot (two-level system) and simultaneously driven by an external pump and a probe ﬁeld. We show that multiple number of transparency windows that appear can be controlled by the QD-cavity coupling strength and also the Fano proﬁles are directly measured by the resonant frequency of the mechanical mode. We also show the optical transition from bistability to tristability/multistability by adjusting the switching threshold of the system parameters. These results can also be used to study frequency optical nonreciprocity and all-optical switches in multi-resonator photonic devices.

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Section: Discussionmentioning

confidence: 99%

Coupling of QD-based PhC nanocavity with two mechanical modes: an approach to tunable optical switching and sensing applications

Yeasmin

Barbhuiya

Bhattacherjee

et al. 2023

J. Opt.

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“…Therefore, according to the Hurwitz criterion [27,28], when R 0 < 1, A 3 > 0, system (1) is locally asymptotically stable at the disease-free equilibrium point E 0 . When R 0 > 1 A 3 < 0, the disease-free equilibrium point is unstable.…”

Section: Stability Of Disease-free Equilibriummentioning

confidence: 99%

Study on SEAI Model of COVID-19 Based on Asymptomatic Infection

Huang,

Xia,

Qin

2024

Axioms

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In this paper, an SEAI epidemic model with asymptomatic infection is studied under the background of mass transmission of COVID-19. First, we use the next-generation matrix method to obtain the basic reproductive number R0 and calculate the equilibrium point. Secondly, when R0<1, the local asymptotic stability of the disease-free equilibrium is proved by Hurwitz criterion, and the global asymptotic stability of the disease-free equilibrium is proved by constructing the Lyapunov function. When R0>1, the system has a unique endemic equilibrium point and is locally asymptotically stable, and it is also proved that the system is uniformly persistent. Then, the application of optimal control theory is carried out, and the expression of the optimal control solution is obtained. Finally, in order to verify the correctness of the theory, the stability of the equilibrium point is numerically simulated and the sensitivity of the parameters of R0 is analyzed. We also simulated the comparison of the number of asymptomatic infected people and symptomatic infected people before and after adopting the optimal control strategy. This shows that the infection of asymptomatic people cannot be underestimated in the spread of COVID-19 virus, and an isolation strategy should be adopted to control the spread speed of the disease.

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“…This study uses the Routh-Hurwitz stability criterion to convert the stability issues in the neighborhood of the operating point to a linear polynomial from a transcendental polynomial (due to the input time delay). The Routh-Hurwitz stability criterion [24] is a necessary and sufficient condition for analyzing the stability of linear time invariant (LTI) dynamical systems. The class of stable systems is bounded by its all-dynamic states as time goes to infinity.…”

Section: Routh-hurwitz Stability Criterion (Patil 2021)mentioning

confidence: 99%

Non-Predictive Model-Free Control of Nonlinear Systems with Unknown Input Time Delay

Zhu

Zhang

2023

Entropy

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This study presents a general framework for the control of unknown dynamic systems with unknown input delay. A concise output feedback control system is structured with tuning stabilization/dynamic response by an output feedback low gain, removing steady state error against step reference with a feedforward gain. A series of stability analyses are presented for the designed control systems, (1) a gain/phase margin theorem is proposed for stability analysis by regulating the feedback gain, and (2) a stability theorem based on rational function approximation of the time delay is presented for dealing with the transcendental polynomial characteristic equations, which is equivalent to the analysis from the algebraic polynomial characteristic equation. Both approaches give coherent results for stability analysis by regulating the feedback gain. The approaches are applicable to nonlinear systems, which are linearizable in the neighborhood of the operating points. The low complexity of the controllers does not require hard analytical derivation/numerical calculations to produce an acceptable control performance for the considered systems. Several representative simulation case studies provide demonstrations of computational experiments against those analytically derived and guidance for potential applications.

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Routh-Hurwitz Criterion for Stability: An Overview and Its Implementation on Characteristic Equation Vectors Using MATLAB

Cited by 10 publications

References 3 publications

Coupling of QD-based PhC nanocavity with two mechanical modes: an approach to tunable optical switching and sensing applications

Coupling of QD-based PhC nanocavity with two mechanical modes: an approach to tunable optical switching and sensing applications

Study on SEAI Model of COVID-19 Based on Asymptomatic Infection

Non-Predictive Model-Free Control of Nonlinear Systems with Unknown Input Time Delay

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