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Global stabilization of discrete‐time linear systems with bounded inputs
Author(s) -
AlvarezRamírez José,
Suárez Rodolfo
Publication year - 1996
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/(sici)1099-1115(199607)10:4/5<409::aid-acs371>3.0.co;2-e
Subject(s) - bounded function , pointwise , eigenvalues and eigenvectors , control theory (sociology) , mathematics , linear system , discrete time and continuous time , exponential stability , algebraic number , state (computer science) , mathematical analysis , nonlinear system , control (management) , computer science , algorithm , statistics , physics , quantum mechanics , artificial intelligence
In this paper we present a technique to stabilize discrete‐time linear systems with bounded inputs. Based on optimal control techniques, we construct a continuous bounded state feedback which leads to global asymptotic stabilization for the case where the open‐loop system has all its eigenvalues with modulus less than or equal to one. If the open‐loop system has eigenvalues with modulus greater than one, a region of attraction of the origin is obtained. The resulting state feedback can be seen as a pointwise linear feedback with state‐dependent gains, which are defined in terms of a non‐linear algebraic equation.