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The extended generalized distance problem in discrete time
Author(s) -
Ionescu Vlad,
Oară Cristian
Publication year - 1998
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(199805)8:6<523::aid-rnc326>3.0.co;2-f
Subject(s) - mathematics , discrete time and continuous time , riccati equation , lyapunov function , factorization , state (computer science) , state space , class (philosophy) , matrix (chemical analysis) , mathematical analysis , differential equation , computer science , algorithm , nonlinear system , statistics , physics , materials science , quantum mechanics , artificial intelligence , composite material
We obtain the class of all solutions to the extended (two block) generalized distance problem for discrete‐time systems by employing the so‐called ‘signature condition’—a generalized Popov theory type argument which parallels the J ‐spectral factorization approach. The novelty is that we derive explicit state‐space formulae in terms of one Riccati and one Lyapunov equation while we remove the usual assumption in the discrete case on the time reversibility (invertibility of the state matrix) of the system to be approximated. © 1998 John Wiley & Sons, Ltd.