From comparison with Ørsted measurements and general considerations of magnetic field predictability, we attribute a root mean square (RMS) uncertainty of 1.3 nT to our candidate model for the main field in 2005, 2.5 nT to the predicted main field in 2010 and 26 nT/a to the predicted secular variation from 2010 to 2015.
Where a single observationally based estimate of water cycle change is stated it is the arithmetic mean of estimates based on the three datasets and the uncertainty is the root mean square of their uncertainties.
Total uncertainty in Fcycle change for the three observational datasets is calculated as the root mean square of the method uncertainty and the data uncertainty in equation (1), which is consistent in the two types of uncertainty are normal.
Therefore, the impulsive equations (2.1 - 2.2 2.1 - 2.2bally exponential robushowtability in mean square for all admissible uncertainties.
Thereby, we can conclude from Theorem 3.2 that the impulsive equations (2.1 - 2.2 2.1 - 2.2bally exponential robushowtability in mean square for all admissible uncertainties (see Figlobally
Definition 1 System (1) and system (9) are said to be globally asymptotically synchronized in the mean square if all parameter uncertainties satisfying the admissible condition (6) and (7), and the trajectories of system (1) and system (9) satisfy lim k → + ∞ E { | y ( k ) − x ( k ) | } = 0.
Theorem 3.2 Assume (H1 - H6) hold and the following condition is satisfied: ( P 2 ) n 2 2 λ min ( A ) ( ν 1 + ν 2 ) < 1, then system (2.1) is exponentially stable in mean square for all admissible uncertainties, that is, e α t E | x ( t ) | 1 2 → 0, as t → ∞.
The aim of this paper is to design a memoryless non-fragile state feedback control law such that the closed-loop system is stochastically asymptotically stable in the mean square for all admissible parameter uncertainties and the closed-loop cost function value is not more than a specified upper bound.
The AFCS map was compared with the validation map through the calculation of three statistical mapping uncertainty measures: root mean square error (RMSE, Eq. 3), bias (Eq. 4), and index of agreement (D, Eq. 5).
HB estimates have smaller mean square errors and account for the uncertainty in the prediction error than corresponding BLUP estimates.
