A new iteration to coupled discrete-time generalized Riccati equations

Ivanov, Ivan Ganchev; Netov, Nikolay

doi:10.1007/s40314-013-0037-3

Cited by 2 publications

(3 citation statements)

References 13 publications

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“…Our numerical experiments confirm the effectiveness of the LMI approach applied to the optimization problems (10) and (11). We have compared the results from these experiments in regard of number of iterations and time (10) performance needs more computational work than LMI problem (11) and thus, LMI method (11) is faster than LMI method (10) (see the CPU times displayed in tables 2 and 3).…”

Section: The Lmi Approachsupporting

confidence: 62%

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Iterations for a General Class of Discrete-Time Riccati-Type Equations: A Survey and Comparison

Ivanov¹

2012

Stochastic Modeling and Control

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Section: The Lmi Approachsupporting

confidence: 62%

“…The convergence result is given by the following theorem: Theorem 2.3. [11] We assume that Γ is a nonnegative matrix and …”

Section: Theorem 22mentioning

confidence: 99%

Iterations for a General Class of Discrete-Time Riccati-Type Equations: A Survey and Comparison

Ivanov¹

2012

Stochastic Modeling and Control

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“…The continuous-time Lyapunov equations can be transformed into CDSEs via the Cayley transformation [11], although determining the optimal Cayley parameter remains a challenge. For other related iterative methods of continuous-time Lyapunov equations, consult [12][13][14][15][16] and the corresponding references.…”

Section: Introductionmentioning

confidence: 99%

Operator Smith Algorithm for Coupled Stein Equations from Jump Control Systems

Yu,

Dong,

2024

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Consider a class of coupled Stein equations arising from jump control systems. An operator Smith algorithm is proposed for calculating the solution of the system. Convergence of the algorithm is established under certain conditions. For large-scale systems, the operator Smith algorithm is extended to a low-rank structured format, and the error of the algorithm is analyzed. Numerical experiments demonstrate that the operator Smith iteration outperforms existing linearly convergent iterative methods in terms of computation time and accuracy. The low-rank structured iterative format is highly effective in approximating the solutions of large-scale structured problems.

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A new iteration to coupled discrete-time generalized Riccati equations

Cited by 2 publications

References 13 publications

Iterations for a General Class of Discrete-Time Riccati-Type Equations: A Survey and Comparison

Iterations for a General Class of Discrete-Time Riccati-Type Equations: A Survey and Comparison

Operator Smith Algorithm for Coupled Stein Equations from Jump Control Systems

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