Non-Fragile Exponential Stability Assignment of Discrete-Time Linear Systems With Missing Data in Actuators
This technical note is concerned with the non-fragile exponential stabilization for a class of discrete-time linear systems with missing data in actuators. The process of missing data is modeled by a discrete-time Markov chain with two state components. When no uncertainty exists in the controllers,...
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| Veröffentlicht in: | IEEE transactions on automatic control 2009-03, Vol.54 (3), p.625-630 |
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| container_title | IEEE transactions on automatic control |
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| creator | Zhan Shu Lam, J. Junlin Xiong |
| description | This technical note is concerned with the non-fragile exponential stabilization for a class of discrete-time linear systems with missing data in actuators. The process of missing data is modeled by a discrete-time Markov chain with two state components. When no uncertainty exists in the controllers, a necessary and sufficient condition, which not only guarantees the exponential stability but also gives a lower bound on the decay rate, is established in terms of linear matrix inequalities (LMIs). Based on this condition, an LMI-based approach is provided to design a non-fragile state-feedback controller such that the closed-loop system is exponentially stable with a prescribed lower bound on the decay rate for the known missing data process and all admissible uncertainties in controllers. A numerical example is provided to show the effectiveness of the theoretical results. |
| doi_str_mv | 10.1109/TAC.2008.2009598 |
| format | Article |
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The process of missing data is modeled by a discrete-time Markov chain with two state components. When no uncertainty exists in the controllers, a necessary and sufficient condition, which not only guarantees the exponential stability but also gives a lower bound on the decay rate, is established in terms of linear matrix inequalities (LMIs). Based on this condition, an LMI-based approach is provided to design a non-fragile state-feedback controller such that the closed-loop system is exponentially stable with a prescribed lower bound on the decay rate for the known missing data process and all admissible uncertainties in controllers. A numerical example is provided to show the effectiveness of the theoretical results.</description><identifier>ISSN: 0018-9286</identifier><identifier>EISSN: 1558-2523</identifier><identifier>DOI: 10.1109/TAC.2008.2009598</identifier><identifier>CODEN: IETAA9</identifier><language>eng</language><publisher>New York, NY: IEEE</publisher><subject>Actuators ; Applied sciences ; Australia ; Computer science; control theory; systems ; Control system analysis ; Control systems ; Control theory ; Control theory. 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The process of missing data is modeled by a discrete-time Markov chain with two state components. When no uncertainty exists in the controllers, a necessary and sufficient condition, which not only guarantees the exponential stability but also gives a lower bound on the decay rate, is established in terms of linear matrix inequalities (LMIs). Based on this condition, an LMI-based approach is provided to design a non-fragile state-feedback controller such that the closed-loop system is exponentially stable with a prescribed lower bound on the decay rate for the known missing data process and all admissible uncertainties in controllers. 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Systems</subject><subject>Controllers</subject><subject>Costs</subject><subject>Decay rate</subject><subject>Exact sciences and technology</subject><subject>Exponential stability</subject><subject>Hydraulic actuators</subject><subject>Linear matrix inequalities</subject><subject>linear matrix inequality (LMI)</subject><subject>Linear systems</subject><subject>Lower bounds</subject><subject>Markov chain</subject><subject>Missing data</subject><subject>non-fragile control</subject><subject>Stability</subject><subject>Sufficient conditions</subject><subject>Uncertainty</subject><issn>0018-9286</issn><issn>1558-2523</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2009</creationdate><recordtype>article</recordtype><sourceid>RIE</sourceid><recordid>eNqFkc1vGyEQxVHUSHGT3ivlgiq1OW0KCyxwtJxPyW0PcdUjAhYc0l3WBSzV_32xbOXQQ3sZNMPvvQE9AN5jdI0xkp9X88V1i5DYF8mkOAEzzJhoWtaSN2CGEBaNbEV3Bt7m_FLbjlI8Az-_TrG5S3odBgdvf2-m6GIJeoBPRZswhLKD85zDOo51DicPb0K2yRXXrMLo4DJEpxN82uXixgx_hPIMv4QqiGt4o4uGIcK5LVtdppQvwKnXQ3bvjuc5-H53u1o8NMtv94-L-bKxlPHSaM8N5x5bJCUymFJDkbdGG2Zsb5jsuO-p6T0hxLCeaC6F6JGnhnFsLUPkHFwdfDdp-rV1uaixPtoNg45u2mYlEemIIFj8lxS82nUdYZX89E-SUEq4YLiCH_4CX6ZtivW_SnS4lVSS_V50gGyack7Oq00Ko047hZHax6lqnGofpzrGWSUfj746Wz34pKMN-VXXYspb3PLKXR644Jx7vaZcci4w-QPumqhh</recordid><startdate>20090301</startdate><enddate>20090301</enddate><creator>Zhan Shu</creator><creator>Lam, J.</creator><creator>Junlin Xiong</creator><general>IEEE</general><general>Institute of Electrical and Electronics Engineers</general><general>The Institute of Electrical and Electronics Engineers, Inc. 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Systems</topic><topic>Controllers</topic><topic>Costs</topic><topic>Decay rate</topic><topic>Exact sciences and technology</topic><topic>Exponential stability</topic><topic>Hydraulic actuators</topic><topic>Linear matrix inequalities</topic><topic>linear matrix inequality (LMI)</topic><topic>Linear systems</topic><topic>Lower bounds</topic><topic>Markov chain</topic><topic>Missing data</topic><topic>non-fragile control</topic><topic>Stability</topic><topic>Sufficient conditions</topic><topic>Uncertainty</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Zhan Shu</creatorcontrib><creatorcontrib>Lam, J.</creatorcontrib><creatorcontrib>Junlin Xiong</creatorcontrib><collection>IEEE All-Society Periodicals Package (ASPP) 2005-present</collection><collection>IEEE All-Society Periodicals Package (ASPP) 1998-Present</collection><collection>IEEE Electronic Library (IEL)</collection><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Electronics & Communications Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><collection>ANTE: Abstracts in New Technology & Engineering</collection><jtitle>IEEE transactions on automatic control</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Zhan Shu</au><au>Lam, J.</au><au>Junlin Xiong</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Non-Fragile Exponential Stability Assignment of Discrete-Time Linear Systems With Missing Data in Actuators</atitle><jtitle>IEEE transactions on automatic control</jtitle><stitle>TAC</stitle><date>2009-03-01</date><risdate>2009</risdate><volume>54</volume><issue>3</issue><spage>625</spage><epage>630</epage><pages>625-630</pages><issn>0018-9286</issn><eissn>1558-2523</eissn><coden>IETAA9</coden><abstract>This technical note is concerned with the non-fragile exponential stabilization for a class of discrete-time linear systems with missing data in actuators. The process of missing data is modeled by a discrete-time Markov chain with two state components. When no uncertainty exists in the controllers, a necessary and sufficient condition, which not only guarantees the exponential stability but also gives a lower bound on the decay rate, is established in terms of linear matrix inequalities (LMIs). Based on this condition, an LMI-based approach is provided to design a non-fragile state-feedback controller such that the closed-loop system is exponentially stable with a prescribed lower bound on the decay rate for the known missing data process and all admissible uncertainties in controllers. A numerical example is provided to show the effectiveness of the theoretical results.</abstract><cop>New York, NY</cop><pub>IEEE</pub><doi>10.1109/TAC.2008.2009598</doi><tpages>6</tpages><oa>free_for_read</oa></addata></record> |
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| ispartof | IEEE transactions on automatic control, 2009-03, Vol.54 (3), p.625-630 |
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| source | IEEE Electronic Library (IEL) |
| subjects | Actuators Applied sciences Australia Computer science control theory systems Control system analysis Control systems Control theory Control theory. Systems Controllers Costs Decay rate Exact sciences and technology Exponential stability Hydraulic actuators Linear matrix inequalities linear matrix inequality (LMI) Linear systems Lower bounds Markov chain Missing data non-fragile control Stability Sufficient conditions Uncertainty |
| title | Non-Fragile Exponential Stability Assignment of Discrete-Time Linear Systems With Missing Data in Actuators |
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