Stability Analysis of Integral Delay Systems with Multiple Delays

This note is concerned with stability analysis of integral delay systems with multiple delays. To study this problem, the well-known Jensen inequality is generalized to the case of multiple terms by introducing an individual slack weighting matrix for each term, which can be optimized to reduce the conservatism. With the help of the multiple Jensen inequalities and by developing a novel linearizing technique, two novel Lyapunov functional based approaches are established to obtain sufficient stability conditions expressed by linear matrix inequalities (LMIs). It is shown that these new conditions are always less conservative than the existing ones. Moreover, by the positive operator theory, a single LMI based condition and a spectral radius based condition are obtained based on an existing sufficient stability condition expressed by coupled LMIs. A numerical example illustrates the effectiveness of the proposed approaches.Comment: 14 page

Fault diagnosis of hydraulic motor based on mathematical morphology filter and sensitive parameters

Aiming at slipper fault diagnosis of hydraulic motor, a fusion method based on mathematical morphology and sensitive parameters is proposed. The method processes advantages of mathematical morphology filtering signals and those of high parameters’ sensitivities to slipper fault. Firstly, a slipper fault signal is filtered by morphological difference operator, and rich characteristic information can be extracted. Secondly, parameters in time and frequency domains are extracted from the signal, and morphological index which is firstly introduced into hydraulic motor fault diagnosis is also included. Lastly, after analyzing sensitivities of the parameters to slipper fault, the fault can be diagnosed effectively, and therefore the fault diagnosis methods based on parameters in time and frequency domains are further enriched

One Fits All: A Unified Synchrotron Model Explains GRBs with FRED-Shaped Pulses

The analysis of gamma-ray burst (GRB) spectra often relies on empirical models like the Band function, which lacks a distinct physical explanation. Previous attempts to couple physical models with observed data have been confined to individual burst studies, where the model is fitted to segmented spectra with independent physical parameters. These approaches frequently fail to explain the spectral evolution, which should be governed by a consistent set of physical conditions. In this study, we propose a novel approach by incorporating the synchrotron radiation model to provide a self-consistent explanation for a selection of single-pulse GRBs. Our sample is carefully chosen to minimize contamination from overlapping pulses, allowing for a comprehensive test of the synchrotron model under a unified physical condition, such as a single injection event of electrons. By tracing the evolution of cooling electrons in a decaying magnetic field, our model predicts a series of time-dependent observed spectra that align well with the observed data. Remarkably, using a single set of physical parameters, our model successfully fits all time-resolved spectra within each burst. Additionally, our model accurately predicts the evolution of some key features of GRBs such as the spectral peak $E_{\rm p}$ and light curve shapes, all of which are consistent with observations. Our findings strongly support the notion that the spectral and temporal evolution in GRB pulses originates from the expansion of the GRB emission region with an initial radius of approximately $10^{15}$ cm, with synchrotron radiation being the underlying emission mechanism.Comment: 25 pages, 18 figures, 4 table

Evaluation of MODIS LAI/FPAR product Collection 6. Part 2: Validation and intercomparison

The aim of this paper is to assess the latest version of the MODIS LAI/FPAR product (MOD15A2H), namely Collection 6 (C6). We comprehensively evaluate this product through three approaches: validation with field measurements, intercomparison with other LAI/FPAR products and comparison with climate variables. Comparisons between ground measurements and C6, as well as C5 LAI/FPAR indicate: (1) MODIS LAI is closer to true LAI than effective LAI; (2) the C6 product is considerably better than C5 with RMSE decreasing from 0.80 down to 0.66; (3) both C5 and C6 products overestimate FPAR over sparsely-vegetated areas. Intercomparisons with three existing global LAI/FPAR products (GLASS, CYCLOPES and GEOV1) are carried out at site, continental and global scales. MODIS and GLASS (CYCLOPES and GEOV1) agree better with each other. This is expected because the surface reflectances, from which these products were derived, were obtained from the same instrument. Considering all biome types, the RMSE of LAI (FPAR) derived from any two products ranges between 0.36 (0.05) and 0.56 (0.09). Temporal comparisons over seven sites for the 2001–2004 period indicate that all products properly capture the seasonality in different biomes, except evergreen broadleaf forests, where infrequent observations due to cloud contamination induce unrealistic variations. Thirteen years of C6 LAI, temperature and precipitation time series data are used to assess the degree of correspondence between their variations. The statistically-significant associations between C6 LAI and climate variables indicate that C6 LAI has the potential to provide reliable biophysical information about the land surface when diagnosing climate-driven vegetation responses.Help from MODIS and VIIRS Science team members is gratefully acknowledged. This work is supported by the MODIS program of NASA and partially funded by the National Basic Research Program of China (Grant No. 2013CB733402) and the key program of NSFC (Grant No. 41331171). Kai Yan gives thanks for the scholarship from the China Scholarship Council. (MODIS program of NASA; 2013CB733402 - National Basic Research Program of China; 41331171 - NSFC; China Scholarship Council

Evaluation of MODIS LAI/FPAR product Collection 6. Part 1: consistency and improvements

As the latest version of Moderate Resolution Imaging Spectroradiometer (MODIS) Leaf Area Index (LAI) and Fraction of Photosynthetically Active Radiation (FPAR) products, Collection 6 (C6) has been distributed since August 2015. This collection is evaluated in this two-part series with the goal of assessing product accuracy, uncertainty and consistency with the previous version. In this first paper, we compare C6 (MOD15A2H) with Collection 5 (C5) to check for consistency and discuss the scale effects associated with changing spatial resolution between the two collections and benefits from improvements to algorithm inputs. Compared with C5, C6 benefits from two improved inputs: (1) L2G–lite surface reflectance at 500 m resolution in place of reflectance at 1 km resolution; and (2) new multi-year land-cover product at 500 m resolution in place of the 1 km static land-cover product. Global and seasonal comparison between C5 and C6 indicates good continuity and consistency for all biome types. Moreover, inter-annual LAI anomalies at the regional scale from C5 and C6 agree well. The proportion of main radiative transfer algorithm retrievals in C6 increased slightly in most biome types, notably including a 17% improvement in evergreen broadleaf forests. With same biome input, the mean RMSE of LAI and FPAR between C5 and C6 at global scale are 0.29 and 0.091, respectively, but biome type disagreement worsens the consistency (LAI: 0.39, FPAR: 0.102). By quantifying the impact of input changes, we find that the improvements of both land-cover and reflectance products improve LAI/FPAR products. Moreover, we find that spatial scale effects due to a resolution change from 1 km to 500 m do not cause any significant differences.Help from MODIS & VIIRS Science team members is gratefully acknowledged. This work is supported by the MODIS program of NASA and partially funded by the National Basic Research Program of China (Grant No. 2013CB733402), the key program of NSFC (Grant No. 41331171) and Chinese Scholarship Council. (MODIS program of NASA; 2013CB733402 - National Basic Research Program of China; 41331171 - NSFC; Chinese Scholarship Council