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A method to solve the discrete-time coupled algebraic Riccati equations. (English) Zbl 1162.65021
The solution of a set of discrete-time coupled algebraic Riccati equations is considered. At first the system is transformed into another system of Riccati equations. Then, two iterative methods for computing a symmetric solution of this system are proposed. In each iteration step one has to solve a Stein equation. Convergence properties of the proposed algorithms are proved. Finally, some numerical examples are given.

65F30Other matrix algorithms
15A24Matrix equations and identities
93C55Discrete-time control systems
65K10Optimization techniques (numerical methods)
Full Text: DOI
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[9] Do Val, J. B.; Geromel, J. C.; Costa, O. L. V.: Solutions for the linear quadratic control problem of Markov jump linear systems. Journal of optimization theory and applications 103, No. 2, 283-311 (1999) · Zbl 0948.49018