{"title":"带脉冲的离散时随机系统的几乎确定的指数稳定性和随机稳定性","authors":"Ting Cai , Pei Cheng , Xing Liu , Mingang Hua","doi":"10.1016/j.cam.2024.116152","DOIUrl":null,"url":null,"abstract":"<div><p>This paper considers the almost sure exponential stability and stochastic stabilization problems of discrete-time stochastic systems (DTSSs) with impulsive effects, where the average impulsive interval is taken into account. By using the average impulsive interval approach and the strong law of large numbers, we not only establish the criteria for almost sure exponential stability of general nonlinear discrete-time impulsive stochastic systems (DTISSs) but also design an exact method of a stochastic perturbation to stabilize a given unstable impulsive discrete-time systems. Adopting the average impulsive interval approach and the strong law of large numbers, we established a criterion for almost sure exponential stability of general nonlinear DTISSs. Furthermore, a method of stochastic perturbation has been developed to stabilize an unstable impulsive discrete-time system. Finally, two simulation examples demonstrate the effectiveness of the derived results.</p></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"453 ","pages":"Article 116152"},"PeriodicalIF":2.1000,"publicationDate":"2024-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Almost sure exponential stability and stochastic stabilization of discrete-time stochastic systems with impulses\",\"authors\":\"Ting Cai , Pei Cheng , Xing Liu , Mingang Hua\",\"doi\":\"10.1016/j.cam.2024.116152\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>This paper considers the almost sure exponential stability and stochastic stabilization problems of discrete-time stochastic systems (DTSSs) with impulsive effects, where the average impulsive interval is taken into account. By using the average impulsive interval approach and the strong law of large numbers, we not only establish the criteria for almost sure exponential stability of general nonlinear discrete-time impulsive stochastic systems (DTISSs) but also design an exact method of a stochastic perturbation to stabilize a given unstable impulsive discrete-time systems. Adopting the average impulsive interval approach and the strong law of large numbers, we established a criterion for almost sure exponential stability of general nonlinear DTISSs. Furthermore, a method of stochastic perturbation has been developed to stabilize an unstable impulsive discrete-time system. Finally, two simulation examples demonstrate the effectiveness of the derived results.</p></div>\",\"PeriodicalId\":50226,\"journal\":{\"name\":\"Journal of Computational and Applied Mathematics\",\"volume\":\"453 \",\"pages\":\"Article 116152\"},\"PeriodicalIF\":2.1000,\"publicationDate\":\"2024-07-22\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Computational and Applied Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0377042724004011\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Computational and Applied Mathematics","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0377042724004011","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Almost sure exponential stability and stochastic stabilization of discrete-time stochastic systems with impulses
This paper considers the almost sure exponential stability and stochastic stabilization problems of discrete-time stochastic systems (DTSSs) with impulsive effects, where the average impulsive interval is taken into account. By using the average impulsive interval approach and the strong law of large numbers, we not only establish the criteria for almost sure exponential stability of general nonlinear discrete-time impulsive stochastic systems (DTISSs) but also design an exact method of a stochastic perturbation to stabilize a given unstable impulsive discrete-time systems. Adopting the average impulsive interval approach and the strong law of large numbers, we established a criterion for almost sure exponential stability of general nonlinear DTISSs. Furthermore, a method of stochastic perturbation has been developed to stabilize an unstable impulsive discrete-time system. Finally, two simulation examples demonstrate the effectiveness of the derived results.
期刊介绍:
The Journal of Computational and Applied Mathematics publishes original papers of high scientific value in all areas of computational and applied mathematics. The main interest of the Journal is in papers that describe and analyze new computational techniques for solving scientific or engineering problems. Also the improved analysis, including the effectiveness and applicability, of existing methods and algorithms is of importance. The computational efficiency (e.g. the convergence, stability, accuracy, ...) should be proved and illustrated by nontrivial numerical examples. Papers describing only variants of existing methods, without adding significant new computational properties are not of interest.
The audience consists of: applied mathematicians, numerical analysts, computational scientists and engineers.