Titlebook: Rational Matrix Equations in Stochastic Control; Tobias Damm Book 2004 Springer-Verlag Berlin Heidelberg 2004 Generalized Lyapunov Equatio

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Solution of the Riccati equation,an abstract form of the Riccati operators met in the Sections 2.1 – 2.3, and the definite and the indefinite constraints mentioned in Remark 2.3.7. Recall that the LQ-stabilization problem and the Bounded Real Lemma lead to Riccati equations with definite constraints, while the disturbance attenuation problem involves an indefinite constraint.

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,Newton’s method, neighbourhood of the actual solution. These results can be simplified and generalized, if the underlying space is ordered and the sequence produced by the iteration can be shown to be monotonic and bounded; this can be the case, for instance, if the nonlinear operator satisfies certain convexity conditions (compare [196] and references therein).

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Rational Matrix Equations in Stochastic Control978-3-540-40001-1Series ISSN 0170-8643 Series E-ISSN 1610-7411

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https://doi.org/10.1007/b10906Generalized Lyapunov Equations; Generalized Riccati Equations; H Infinity Control; Matrix; Positive Oper

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Hermitian matrices and Schur complements,Throughout the text, . denotes either the field of real or the field of numbers. For simplicity we write .. rather than .. for the transpose of a real matrix and call a real symmetric matrix Hermitian. At some occasions we still need the notation .. for the transpose of a real or complex matrix – without conjugation.

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