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Zbl 1190.65066
Ivanov, Ivan Ganchev
Stein iterations for the coupled discrete-time Riccati equations. (English)
[J] Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 71, No. 12, A, 6244-6253 (2009). ISSN 0362-546X

Markovian jump linear systems (MJLS) are a class of models used to represent discrete jumps in continuous dynamics. This paper deals with iterative algorithms for computing solutions of a set of coupled algebraic Riccati equations that appears in quadratic optimal control problems for discrete-time MJLS. Two algorithms using decoupled Stein matrix equations are presented. A numerical example illustrates the proposed methods.
[Edgar Pereira (Covilha)]

MSC 2000:: *65F30 Other matrix algorithms
65F10 Iterative methods for linear systems
93C55 Discrete-time control systems
65K10 Optimization techniques (numerical methods)
49N10 Linear-quadratic optimal control problems
15A24 Matrix equations

Keywords: Markovian jump linear system; Riccati matrix equation; Stein matrix equation; iterative method; discrete-time Riccati equations; positive definite solution; algorithm; quadratic optimal control problems; numerical example

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Zentralblatt MATH Berlin [Germany]