New Stability Criteria for Discrete Linear Systems Based on Orthogonal Polynomials

Garza, Luis E.; Martínez, Noé; Romero, Gerardo

doi:10.3390/math8081322

Cited by 2 publications

(1 citation statement)

References 31 publications

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“…Furthermore, the dynamic system described by equation [20], is asymptotically stable according to [21,22] when the Stodola stability condition is met and all major minors (subdeterminants) of the Hurwitz matrix Hi are positive:…”

Section: Methodsmentioning

confidence: 99%

Financial Stability Control for Business Sustainability: A Case Study from Food Production

Macak¹

2022

Mathematics

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Conventional financial management methods, based on extrapolation approaches to financial analysis, often reach their limits due to violations of stationary controlled financial variables, for example, interventions in the economy and social life necessary to manage the COVID-19 pandemic. Therefore, we have created a procedure for controlling financial quantities, which respects the non-stationarity of the controlled quantity using the maximum control deviation covering the confidence interval of a random variable or random vector. For this interval, we then determined the algebraic criteria of the transfer functions using the Laplace transform. For the Laplace transform, we determined the theorem on the values of the stable roots of the characteristic equation, including the deductive proof. This theorem is directly usable for determining the stability of the management for selected financial variables. For the practical application, we used the consistency of the stable roots of the characteristic equation with the Stodola and Hurwitz stability conditions. We demonstrated the procedure for selected quantities of financial management in food production. In conclusion, we proposed a control mechanism for the convergence of regulatory deviation using a combination of proportional and integration schemes. We also determined the diversification of action interventions (into development, production, and marketing) using a factorial design.

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Section: Methodsmentioning

confidence: 99%