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On computing the stabilizing solution of a class of discrete‐time periodic Riccati equations
Author(s) -
Dragan Vasile,
Aberkane Samir,
Ivanov Ivan G.
Publication year - 2013
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.3131
Subject(s) - riccati equation , discrete time and continuous time , sign (mathematics) , quadratic equation , mathematics , algebraic riccati equation , convergence (economics) , linear quadratic regulator , class (philosophy) , linear quadratic gaussian control , rate of convergence , optimal control , computer science , mathematical optimization , mathematical analysis , differential equation , key (lock) , statistics , geometry , computer security , artificial intelligence , economic growth , economics
Summary This paper addresses the problem of solving a class of periodic discrete‐time Riccati equation with an indefinite sign of its quadratic term. Such an equation is closely related to the so‐called full‐information H ∞ control of discrete‐time periodic systems. A globally convergent iterative algorithm with a local quadratic convergence rate is proposed for this purpose. An application to the problem of H ∞ filtering of discrete‐time periodic systems is also developed and illustrated via a numerical example. Copyright © 2013 John Wiley & Sons, Ltd.