Strict anisotropic norm bounded real lemma in terms of matrix inequalities

This paper is aimed at extending the H _∞ Bounded Real Lemma to stochastic systems under random disturbances with imprecisely known probability distributions. The statistical uncertainty is measured in the terms of information theory using the mean anisotropy functional. The disturbance attenuation capabilities of the system are quantified by the anisotropic norm which is a stochastic counterpart of the H _∞ norm. A state-space sufficient criterion for the anisotropic norm of a linear discrete time invariant system to be bounded by a given threshold value is derived. The resulting Strict Anisotropic Norm Bounded Real Lemma involves an inequality on the determinant of a positive definite matrix and a linear matrix inequality. These convex constraints can be approximated by two linear matrix inequalities.     

Analysis of n(87Sr)/n(86Sr), δ88Sr/86SrSRM987 and elemental pattern to characterise groundwater and recharge of saline ponds in a clastic aquifer in East Austria

Elemental and isotopic pattern of n(⁸⁷Sr)/n(⁸⁶Sr) and δ⁸⁸Sr/⁸⁶Sr_SRM987 were used to characterise groundwater and recharge of saline ponds in a clastic aquifer in East Austria. Therefore, shallow, artesian and thermal groundwaters of the investigated aquifer along with rainfall and rivers were analysed using (MC) ICP-MS. The n(⁸⁷Sr)/n(⁸⁶Sr) ratio and elemental pattern changed with aquifer depth as a result of progressing bedrock leaching and dissolution with increasing groundwater residence time. The n(⁸⁷Sr)/n(⁸⁶Sr) ratio of shallow groundwater below saline ponds of 0.71019?±?0.00044 was significantly different from thermal groundwater of 0.71205?±?0.00035 (U, k?=?2). In contrast to previous theories, this result suggested no recharge of saline ponds by upwelling paleo-seawater. Isotope pattern deconvolution revealed that rainfall accounted to about 60% of the n(⁸⁷Sr)/n(⁸⁶Sr) ratio of shallow groundwater below saline ponds. The δ⁸⁸Sr/⁸⁶Sr_SRM987 values of groundwater decreased from about 0.25 ‰ in most shallow, to predominantly negative values of about –0.24 ‰ in artesian groundwater. This result indicated leaching and dissolution of weathered minerals. In turn, the δ⁸⁸Sr/⁸⁶Sr_SRM987 of deep thermal groundwater showed positive values of about 0.12 ‰, which suggested removal of ⁸⁶Sr from solution by carbonate precipitation. These results highlight the potential of δ⁸⁸Sr/⁸⁶Sr_SRM987 signature as an additional geochemical tracer.     

A solution to anisotropic suboptimal filtering problem by convex optimization

This paper considers a robust filtering problem for a linear discrete time invariant system with measured and estimated outputs. The system is exposed to random disturbances with imprecisely known distributions generated by an unknown stable shaping filter from the Gaussian white noise. The stochastic uncertainty of the input disturbance is measured by the mean anisotropy functional. The estimation error is quantified by the anisotropic norm which is a stochastic analogue of the H _∞ norm. A sufficient condition for an estimator to exist and ensure that the error is less than a given threshold value is derived in form of a convex inequality on the determinant of a positive definite matrix and two linear matrix inequalities. The suboptimal problem setting results to a set of the estimators ensuring the anisotropic norm of the error to be strictly bounded thereby providing some additional degree of freedom to impose some additional constraints on the estimator performance specification.