and filtering for linear systems with uncertain Markov transitions

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• 作者：Xianwei Li^a ; ^{lixianwei1985@gmail.com" class="auth_mail" title="E-mail the corresponding author}Author Vitae ; James Lam^b ; ^{james.lam@hku.hk" class="auth_mail" title="E-mail the corresponding author}Author Vitae ; Huijun Gao^a ; ¹ ; ^{huijungao@gmail.com" class="auth_mail" title="E-mail the corresponding author}Author Vitae ; Junlin Xiong^c ; ^{junlin.xiong@gmail.com" class="auth_mail" title="E-mail the corresponding author}Author Vitae
• 关键词：H&infin ; H&infin ; filtering ; H2H2 filtering ; Markovian jump linear system ; Uncertain transition probability ; Linear matrix inequality
• 刊名：Automatica
• 出版年：2016
• 出版时间：May 2016
• 年：2016
• 卷：67
• 期：Complete
• 页码：252-266
• 全文大小：783 K

文摘

This paper is concerned with class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0005109816000170&_mathId=si6.gif&_user=111111111&_pii=S0005109816000170&_rdoc=1&_issn=00051098&md5=c401dfba00444a62f7e61af6454b29b1" title="Click to view the MathML source">H_∞class="mathContainer hidden">class="mathCode">$H_{\infty }$ and class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0005109816000170&_mathId=si20.gif&_user=111111111&_pii=S0005109816000170&_rdoc=1&_issn=00051098&md5=60e39c598b9556967ceb75e563135906" title="Click to view the MathML source">H₂class="mathContainer hidden">class="mathCode">$H_2$ filtering for Markovian jump linear systems with uncertain transition probabilities. Motivated by the fact that the existing results either impose severe restrictions on some key matrices or introduce some unnecessary matrix variables, this paper is focused on developing a new approach to systematically relax these restrictions for filter design. By applying a novel technique to eliminate the product terms between the Lyapunov matrices and the filter parameters, an improved condition is first obtained for analyzing the class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0005109816000170&_mathId=si6.gif&_user=111111111&_pii=S0005109816000170&_rdoc=1&_issn=00051098&md5=c401dfba00444a62f7e61af6454b29b1" title="Click to view the MathML source">H_∞class="mathContainer hidden">class="mathCode">$H_{\infty }$ performance of the filtering error system. Then sufficient conditions in terms of linear matrix inequalities are presented for designing filters with a guaranteed class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0005109816000170&_mathId=si6.gif&_user=111111111&_pii=S0005109816000170&_rdoc=1&_issn=00051098&md5=c401dfba00444a62f7e61af6454b29b1" title="Click to view the MathML source">H_∞class="mathContainer hidden">class="mathCode">$H_{\infty }$ filtering performance level. The proposed method is further extended to class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0005109816000170&_mathId=si20.gif&_user=111111111&_pii=S0005109816000170&_rdoc=1&_issn=00051098&md5=60e39c598b9556967ceb75e563135906" title="Click to view the MathML source">H₂class="mathContainer hidden">class="mathCode">$H_2$ filtering. Theoretical analyses followed by a few numerical examples show that the proposed filter design method outperforms some existing results with respect to reduction of conservatism or variables needed for computation. The filter design problems for both continuous-time and discrete-time Markovian jump linear systems are addressed in a unified framework.