Premium
Linear systems with bounded inputs: global stabilization with eigenvalue placement
Author(s) -
Suárez Rodolfo,
ÁlvarezRamírez José,
SolísDaun Julio
Publication year - 1997
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(199709)7:9<835::aid-rnc216>3.0.co;2-p
Subject(s) - bounded function , control theory (sociology) , eigenvalues and eigenvectors , linear system , nonlinear system , scalar (mathematics) , mathematics , feedback control , neighbourhood (mathematics) , linear quadratic regulator , full state feedback , nonlinear control , controller (irrigation) , controllability , control (management) , computer science , optimal control , mathematical optimization , mathematical analysis , engineering , control engineering , physics , geometry , agronomy , quantum mechanics , artificial intelligence , biology
This work presents a technique for obtaining a bounded continuous feedback control function which stabilizes a linear system in a certain region. If the open‐loop system has no eigenvalues with positive real part, the region of attraction of the resulting closed‐loop system is all ℝ n , i.e., the feedback control is a global stabilizer; otherwise, the region contains an invariant (‘cylindric‐like’) set where the controller does not saturate. The proposed control is a linear‐like feedback control with state‐dependent gains. The gains become implicitly defined in terms of a nonlinear scalar equation. The control function coincides in an ellipsoidal neighbourhood of the origin with a linear feedback law which is a solution of a linear quadratic regulator problem. This design allows eigenvalue placement in a specified region. © 1997 by John Wiley & Sons, Ltd.