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High gain observers applied to problems in the stabilization of uncertain linear systems, disturbance attenuation and N ∞ optimization
Author(s) -
Petersen Ian R.,
Hollot Christopher V.
Publication year - 1988
Publication title -
international journal of adaptive control and signal processing
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.73
H-Index - 66
eISSN - 1099-1115
pISSN - 0890-6327
DOI - 10.1002/acs.4480020409
Subject(s) - control theory (sociology) , attenuation , transfer function , linear system , disturbance (geology) , minimum phase , norm (philosophy) , observer (physics) , upper and lower bounds , mathematics , optimization problem , function (biology) , computer science , control (management) , mathematical optimization , engineering , physics , mathematical analysis , paleontology , electrical engineering , quantum mechanics , artificial intelligence , evolutionary biology , law , political science , optics , biology
In recent years, a number of approaches have been developed for solving the following problem in linear systems theory: design a state feedback control so that the norm of a specified transfer function is less than a given bound over all frequencies. This paper deals with the case in which not all systems states can be measured. It shows that if a certain minimum phase condition is satisfied, then the transfer function bound achievable using state feedback can be asymptotically recovered using a high gain observer. These results have application to the problems of disturbance attenuation, H ∞ optimization and the stabilization of uncertain linear systems.