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Ivanov, Ivan Ganchev

Stein iterations for the coupled discrete-time Riccati equations. (English) Zbl 1190.65066

Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 71, No. 12, 6244-6253 (2009).
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.
Reviewer: Edgar Pereira (Covilha)

Cited in 5 Documents

MSC:

65F30 Other matrix algorithms (MSC2010)
65F10 Iterative numerical methods for linear systems
93C55 Discrete-time control/observation systems
65K10 Numerical optimization and variational techniques
49N10 Linear-quadratic optimal control problems
15A24 Matrix equations and identities

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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\textit{I. G. Ivanov}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 71, No. 12, 6244--6253 (2009; Zbl 1190.65066)
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References:

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