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Then, the desired state estimator, which can ensure the estimation error dynamics to be globally asymptotically robustly stochastically stable, is designed from the solutions of LMIs.
By resorting to the Lyapunov functional method and some stochastic analysis tools, it is shown that if a set of linear matrix inequalities (LMIs) is feasible, the desired state estimator, that can ensure the estimation error dynamics to be globally robustly asymptotically stable in the mean square, exists.
Then, the explicit expression of the desired estimator is shown to ensure the estimation error dynamics to be robustly exponentially stable in the mean square and a prescribed H∞ disturbance rejection attenuation is guaranteed for the addressed system.
Besides, the weighting matrix is set adaptively according to the sub-carrier power to ensure the estimation accuracy.
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To ensure the estimations are statistically significant, we performed the same experiment (EM fitting with 10 repetitions) 10 times and then finally estimated the average runtime, total error, and the error associated with the smallest cluster.
Sufficient conditions for ensuring the estimation error convergence are derived employing the LMI framework.
Therefore, we proposed a new technique (early termination of block matching) to further reduce the computational complexity under the premise of ensuring the estimation accuracy.
A strategy to soften this problem is to perform simultaneous parameters selection and estimation, which ensures the estimation of the selected parameters (e.g., Secchi et al. [ 14], Wu et al. [ 15]; Wu et al. [ 16]; McLean et al. [ 17]; Alberton et al. [ 18]).
We take a conservative approach that minimizes gaps in the supermatrix and use several ways to carefully distinguish orthologs from paralogs to assemble a high quality phylogenomic data set, ensuring the estimation of a robust and accurate tree, including the placement of the deeper lineages in the tree.
Two sets of Riccati difference equations are introduced to ensure the H∞ estimation performance of the designed filter.
By utilizing Lyapunov stability theory and linear matrix inequality techniques, sufficient conditions are established which can ensure the augmented estimation error system to be asymptotically stable.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com