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Konstantinov, M. M.; Angelova, Vera

doi:10.1023/a:1018903104476

Cited by 6 publications

(3 citation statements)

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“…The results obtained for j = 12, 10, 8, 6, 4, 2 are listed in Table 4 for α = 0 and in Table 5 for α = 5. Comparing the results for the bound (34) and (35) to these for the bound (8)- (13) given in Tables 2 and 3, it is seen that the two bounds are of the same size of the domain of validity. The bound ( 8)-( 13) from Theorem 1 is superior to the bound (34) and (35) from Theorem 2 with respect of closeness to the estimated quantity.…”

Section: Numerical Examplesmentioning

confidence: 88%

“…To estimate the sensitivity of the problem (24), we consider the strategies proposed in [13]. We represent the calculated perturbed solution to (24) with collection of data coefficients Z m = T A m , T D m , S m , F m , G m , Y 0 ) as the exact solution to a slightly perturbed problem with collection of data coefficients Z m + ∆Z m .…”

Section: Sensitivity Of Low-dimensional Approximate Solutions To Larg...mentioning

confidence: 99%

“…First, we study the sensitivity of the solution X(t) to (1) to perturbations in the matrix coefficients A, D, Q, S, X 0 . It is done by adapting the bounds established for the symmetric differential Riccati equation, obtained by [12,13] to the nonsymmetric Riccati equation, which show good upper sensitivity. The perturbation bounds are very important for interpreting a numerically computed solution.…”

Section: Introduction and Notationsmentioning

confidence: 99%

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Sensitivity of the Solution to Nonsymmetric Differential Matrix Riccati Equation

2021

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Nonsymmetric differential matrix Riccati equations arise in many problems related to science and engineering. This work is focusing on the sensitivity of the solution to perturbations in the matrix coefficients and the initial condition. Two approaches of nonlocal perturbation analysis of the symmetric differential Riccati equation are extended to the nonsymmetric case. Applying the techniques of Fréchet derivatives, Lyapunov majorants and fixed-point principle, two perturbation bounds are derived: the first one is based on the integral form of the solution and the second one considers the equivalent solution to the initial value problem of the associated differential system. The first bound is derived for the nonsymmetric differential Riccati equation in its general form. The perturbation bound based on the sensitivity analysis of the associated linear differential system is formulated for the low-dimensional approximate solution to the large-scale nonsymmetric differential Riccati equation. The two bounds exploit the existing sensitivity estimates for the matrix exponential and are alternative.

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Section: Numerical Examplesmentioning

confidence: 88%

Section: Sensitivity Of Low-dimensional Approximate Solutions To Larg...mentioning

confidence: 99%

Section: Introduction and Notationsmentioning

confidence: 99%

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