Continuous and Discrete Time Stability State Space

Abstract

We study a new class of stochastic delay systems simultaneously containing continuousand discrete-time components. To analyze various types of stability of such systems, a modified regularization method is proposed and justified. It is based on the choice of an auxiliary equation and an application of the theory of positively invertible matrices. This method was developed for deterministic functional-differential equations by N.V. Azbelev and his students. We give sufficient conditions for the moment stability of solutions both in terms of the positive invertibility of matrices constructed from the system parameters and in terms of the coefficients. These conditions are verified for specific systems of equations.

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ACKNOWLEDGMENTS

The authors express their gratitude to the referee, whose suggestions contributed to a significant improvement in the presentation.

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Authors and Affiliations

1. Dagestan Federal Research Center, Russian Academy of Sciences, Makhachkala, Dagestan, 367000, Russia

   R. I. Kadiev

2. Dagestan State University, Makhachkala, Dagestan, 367015, Russia

   R. I. Kadiev

3. Norwegian University of Life Sciences, As, 1433, Norway

   A. V. Ponosov

Corresponding authors

Correspondence to R. I. Kadiev or A. V. Ponosov.

Additional information

Translated by V. Potapchouck

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Kadiev, R.I., Ponosov, A.V. Stability Analysis of Solutions of Continuous–Discrete Stochastic Systems with Aftereffect by a Regularization Method. Diff Equat 58, 433–454 (2022). https://doi.org/10.1134/S0012266122040012

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• Received: 24 March 2021

• Revised: 07 February 2022

• Accepted: 09 March 2022

• Published: 03 August 2022

• Issue Date: April 2022

• DOI : https://doi.org/10.1134/S0012266122040012

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