Partial Stability of Linear Hybrid Discrete–Continuous Itô Systems with Aftereffect
This paper offers several new sufficient conditions of the partial moment stability of linear hybrid stochastic systems with delay. Despite its potential applications in economics, biology and physics, this problem seems to have not been addressed before. A number of general theorems on the partial...
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MDPI AG
2025-01-01
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| author | Ramazan I. Kadiev Arcady Ponosov |
| author_facet | Ramazan I. Kadiev Arcady Ponosov |
| author_sort | Ramazan I. Kadiev |
| collection | DOAJ |
| description | This paper offers several new sufficient conditions of the partial moment stability of linear hybrid stochastic systems with delay. Despite its potential applications in economics, biology and physics, this problem seems to have not been addressed before. A number of general theorems on the partial moment stability of stochastic hybrid systems are proven herein by applying a specially designed regularization method, based on the connections between Lyapunov stability and input-to-state stability, which are well known in control theory. Based on the results obtained for stochastic hybrid systems, some new conditions of the partial stability of deterministic hybrid systems are derived as well. All stability conditions are conveniently formulated in terms of the coefficients of the systems. A numerical example illustrates the feasibility of the suggested framework. |
| format | Article |
| id | doaj-art-04f7d8aa6f7e462bb18a2697f5707b6a |
| institution | DOAJ |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | MDPI AG |
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| series | Mathematics |
| spelling | doaj-art-04f7d8aa6f7e462bb18a2697f5707b6a2025-08-20T03:12:35ZengMDPI AGMathematics2227-73902025-01-0113339710.3390/math13030397Partial Stability of Linear Hybrid Discrete–Continuous Itô Systems with AftereffectRamazan I. Kadiev0Arcady Ponosov1Dagestan Research Center of the Russian Academy of Sciences & Department of Mathematics, Dagestan State University, 367005 Makhachkala, RussiaDepartment of Mathematics, Norwegian University of Life Sciences, 1432 Aas, NorwayThis paper offers several new sufficient conditions of the partial moment stability of linear hybrid stochastic systems with delay. Despite its potential applications in economics, biology and physics, this problem seems to have not been addressed before. A number of general theorems on the partial moment stability of stochastic hybrid systems are proven herein by applying a specially designed regularization method, based on the connections between Lyapunov stability and input-to-state stability, which are well known in control theory. Based on the results obtained for stochastic hybrid systems, some new conditions of the partial stability of deterministic hybrid systems are derived as well. All stability conditions are conveniently formulated in terms of the coefficients of the systems. A numerical example illustrates the feasibility of the suggested framework.https://www.mdpi.com/2227-7390/13/3/397stochastic hybrid equationsinverse-positive matricesdelay effects |
| spellingShingle | Ramazan I. Kadiev Arcady Ponosov Partial Stability of Linear Hybrid Discrete–Continuous Itô Systems with Aftereffect Mathematics stochastic hybrid equations inverse-positive matrices delay effects |
| title | Partial Stability of Linear Hybrid Discrete–Continuous Itô Systems with Aftereffect |
| title_full | Partial Stability of Linear Hybrid Discrete–Continuous Itô Systems with Aftereffect |
| title_fullStr | Partial Stability of Linear Hybrid Discrete–Continuous Itô Systems with Aftereffect |
| title_full_unstemmed | Partial Stability of Linear Hybrid Discrete–Continuous Itô Systems with Aftereffect |
| title_short | Partial Stability of Linear Hybrid Discrete–Continuous Itô Systems with Aftereffect |
| title_sort | partial stability of linear hybrid discrete continuous ito systems with aftereffect |
| topic | stochastic hybrid equations inverse-positive matrices delay effects |
| url | https://www.mdpi.com/2227-7390/13/3/397 |
| work_keys_str_mv | AT ramazanikadiev partialstabilityoflinearhybriddiscretecontinuousitosystemswithaftereffect AT arcadyponosov partialstabilityoflinearhybriddiscretecontinuousitosystemswithaftereffect |