Premium
Optimal l ∞ disturbance attenuation and global stabilization of linear systems with bounded control
Author(s) -
Sznaier Mario,
Suárez Rodolfo,
Miani Stefano,
AlvarezRamírez José
Publication year - 1999
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/(sici)1099-1239(199908)9:10<659::aid-rnc428>3.0.co;2-m
Subject(s) - bounded function , control theory (sociology) , attenuation , nonlinear system , disturbance (geology) , neighbourhood (mathematics) , linear system , control (management) , open loop controller , computer science , mathematics , engineering , closed loop , control engineering , physics , mathematical analysis , paleontology , artificial intelligence , optics , quantum mechanics , biology
This papers addresses the problem of globally minimizing the worst‐case response to persistent l ∞ bounded disturbances in linear systems with bounded control action. The main result of the paper shows that in the state‐feedback case the best performance among all stabilizing controllers (possibly discontinuous, nonlinear time varying) is achieved by a memoryless, continuous, feedback control law. In the case of open‐loop stable plants the proposed control law renders the system globally stable and provides the best possible l ∞ attenuation in every neighbourhood of the origin. In the case of open‐loop unstable plants this law optimizes performance in the region where a finite l ∞ gain can be achieved. Copyright © 1999 John Wiley & Sons, Ltd.