A Small-Gain Condition for Interconnections of ISS Systems With Mixed ISS Characterizations
We consider interconnected nonlinear systems with external inputs, where each of the subsystems is assumed to be input-to-state stable (ISS). Sufficient conditions of small-gain type are provided guaranteeing that the interconnection is ISS with respect to the external input. To this end we extend r...
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| Veröffentlicht in: | IEEE transactions on automatic control 2011-06, Vol.56 (6), p.1247-1258 |
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| container_title | IEEE transactions on automatic control |
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| creator | Dashkovskiy, S Kosmykov, M Wirth, F R |
| description | We consider interconnected nonlinear systems with external inputs, where each of the subsystems is assumed to be input-to-state stable (ISS). Sufficient conditions of small-gain type are provided guaranteeing that the interconnection is ISS with respect to the external input. To this end we extend recently obtained small-gain theorems to a more general type of interconnections. The small-gain theorem provided here is applicable to situations where the ISS conditions are formulated differently for each subsystem and are either given in the maximization or the summation sense. Furthermore, it is shown that the conditions are compatible in the sense that it is always possible to transform sum formulations to maximum formulations without destroying a given small-gain condition. An example shows the advantages of our results in comparison with the known ones. |
| doi_str_mv | 10.1109/TAC.2010.2080110 |
| format | Article |
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Sufficient conditions of small-gain type are provided guaranteeing that the interconnection is ISS with respect to the external input. To this end we extend recently obtained small-gain theorems to a more general type of interconnections. The small-gain theorem provided here is applicable to situations where the ISS conditions are formulated differently for each subsystem and are either given in the maximization or the summation sense. Furthermore, it is shown that the conditions are compatible in the sense that it is always possible to transform sum formulations to maximum formulations without destroying a given small-gain condition. An example shows the advantages of our results in comparison with the known ones.</description><subject>Applied sciences</subject><subject>Computer science; control theory; systems</subject><subject>Construction industry</subject><subject>Control system analysis</subject><subject>Control systems</subject><subject>Control theory. 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Systems</topic><topic>Exact sciences and technology</topic><topic>Gain</topic><topic>Indexes</topic><topic>large-scale systems</topic><topic>Lyapunov method</topic><topic>Lyapunov methods</topic><topic>Nonlinear systems</topic><topic>Stability criteria</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Dashkovskiy, S</creatorcontrib><creatorcontrib>Kosmykov, M</creatorcontrib><creatorcontrib>Wirth, F R</creatorcontrib><collection>IEEE All-Society Periodicals Package (ASPP) 2005-present</collection><collection>IEEE All-Society Periodicals Package (ASPP) 1998-Present</collection><collection>IEEE/IET Electronic Library (IEL)</collection><collection>Pascal-Francis</collection><collection>CrossRef</collection><jtitle>IEEE transactions on automatic control</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Dashkovskiy, S</au><au>Kosmykov, M</au><au>Wirth, F R</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A Small-Gain Condition for Interconnections of ISS Systems With Mixed ISS Characterizations</atitle><jtitle>IEEE transactions on automatic control</jtitle><stitle>TAC</stitle><date>2011-06-01</date><risdate>2011</risdate><volume>56</volume><issue>6</issue><spage>1247</spage><epage>1258</epage><pages>1247-1258</pages><issn>0018-9286</issn><eissn>1558-2523</eissn><coden>IETAA9</coden><abstract>We consider interconnected nonlinear systems with external inputs, where each of the subsystems is assumed to be input-to-state stable (ISS). 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| subjects | Applied sciences Computer science control theory systems Construction industry Control system analysis Control systems Control theory. Systems Exact sciences and technology Gain Indexes large-scale systems Lyapunov method Lyapunov methods Nonlinear systems Stability criteria |
| title | A Small-Gain Condition for Interconnections of ISS Systems With Mixed ISS Characterizations |
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