{"title":"A Bounded Real Lemma for Discrete-time Systems with Stochastic Dynamics","authors":"Yuji Nagira, Y. Hosoe, T. Hagiwara","doi":"10.9746/sicetr.55.816","DOIUrl":null,"url":null,"abstract":"The bounded real lemma for deterministic linear time-invariant systems is known as one of the most important tools in robust stability analysis. A counterpart for systems with stochastic dynamics is considered to be also important, and A.E. Bouhtouri, et al. (1998) have derived it for discrete-time systems with state-dependent noise. However, the class of the systems is restrictive, and has room for generalization. The purpose of this paper is to show the sufficiency for a new bounded real lemma for more general systems with stochastic dynamics determined by an i.i.d. process. The validity of the lemma is demonstrated with numerical examples.","PeriodicalId":416828,"journal":{"name":"Transactions of the Society of Instrument and Control Engineers","volume":"4 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Transactions of the Society of Instrument and Control Engineers","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.9746/sicetr.55.816","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
The bounded real lemma for deterministic linear time-invariant systems is known as one of the most important tools in robust stability analysis. A counterpart for systems with stochastic dynamics is considered to be also important, and A.E. Bouhtouri, et al. (1998) have derived it for discrete-time systems with state-dependent noise. However, the class of the systems is restrictive, and has room for generalization. The purpose of this paper is to show the sufficiency for a new bounded real lemma for more general systems with stochastic dynamics determined by an i.i.d. process. The validity of the lemma is demonstrated with numerical examples.