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Output feedback control for quadratic systems: A Lyapunov function approach
Author(s) -
Tognetti Eduardo S.,
Jungers Marc,
Calliero Taís R.
Publication year - 2021
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/rnc.5435
Subject(s) - control theory (sociology) , lyapunov function , linearization , controller (irrigation) , state (computer science) , quadratic equation , mathematics , polytope , state space , nonlinear system , exponential stability , state vector , control lyapunov function , feedback linearization , computer science , mathematical optimization , lyapunov redesign , control (management) , algorithm , statistics , physics , geometry , quantum mechanics , artificial intelligence , discrete mathematics , classical mechanics , agronomy , biology
This article deals with the design of quadratic and linear dynamic output feedback controllers for quadratic systems to ensure, on the one hand, local exponential stability of the origin in the closed‐loop form and, on the other hand, to increase an estimate of the basin of attraction of the origin as large as possible. The introduction of a quadratic term in the controller allows us to consider a controller in the same class of dynamics as the studied system. Here, our approach is to consider a Lyapunov function with respect to the extended state gathering the states of the system and the controller. The induced nonlinear inequalities are treated thanks to an auxiliary vector repeating the extended state adequately and by combining distinct linearization techniques to finally obtain linear matrix inequalities. For comparison purposes, we also provide another approach characterizing the extended state as belonging to a polytope in the state space. Numerical examples illustrate the results.