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Robust ℋ︁ 2 static output feedback design starting from a parameter‐dependent state feedback controller for time‐invariant discrete‐time polytopic systems
Author(s) -
Moreira Heber R.,
Oliveira Ricardo C. L. F.,
Peres Pedro L. D.
Publication year - 2011
Publication title -
optimal control applications and methods
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.458
H-Index - 44
eISSN - 1099-1514
pISSN - 0143-2087
DOI - 10.1002/oca.916
Subject(s) - control theory (sociology) , output feedback , discrete time and continuous time , full state feedback , lyapunov function , robust control , linear matrix inequality , controller (irrigation) , computer science , lti system theory , state (computer science) , matrix (chemical analysis) , linear system , mathematics , control (management) , mathematical optimization , control system , engineering , algorithm , nonlinear system , materials science , artificial intelligence , mathematical analysis , composite material , biology , quantum mechanics , agronomy , statistics , physics , electrical engineering
Abstract This paper investigates the problem of computing robust ℋ 2 static output feedback controllers for discrete‐time uncertain linear systems with time‐invariant parameters lying in polytopic domains. A two stages design procedure based on linear matrix inequalities is proposed as the main contribution. First, a parameter‐dependent state feedback controller is synthesized and the resulting gains are used as an input condition for the second stage, which designs the desired robust static output feedback controller with an ℋ 2 guaranteed cost. The conditions are based on parameter‐dependent Lyapunov functions and, differently from most of existing approaches, can also cope with uncertainties in the output control matrix. Numerical examples, including a mass–spring system, illustrate the advantages of the proposed procedure when compared with other methods available in the literature. Copyright © 2009 John Wiley & Sons, Ltd.