Stability and stabilisation of Markovian jump systems under fast switching: an averaging approach

ABSTRACTThis paper addresses the problems of stability and stabilisation of Markovian jump systems(MJSs) with fast switching. First, a novel model by applying an averaging approach to the fastswitching is proposed. Then, a new method for constructing an auxiliary system is given to makethe stability analysis. It is proved that the stability of the originally fast switching MJS couldbe guaranteed by an MJS with an average switching, if the fast switching achieves its averageapproximation sufficiently fast. Based on the proposed results, some extensions about generally stabilising controllers are considered, where the fault-tolerant situation is involved too.All the conditions are presented in terms of LMIs. Finally, two numerical examples are used todemonstrate the effectiveness and superiority of the method.

Variation in the methods leads to variation in the interpretation of biodiversity-ecosystem multifunctionality relationships

Aims Biodiversity is often positively related to the capacity of an ecosystem to provide multiple functions simultaneously(i.e.multifunctionality).However,there is some controversy over whether biodiversity–multifunctionality relationships depend on the number of functions considered.Particularly,investigators have documented contrasting findings that the effects of biodiversity on ecosystem multifunctionality do not change or increase with the number of ecosystem functions.Here,we provide some clarity on this issue by examining the statistical underpinnings of different multifunctionality metrics.Methods We used simulations and data from a variety of empirical studies conducted across spatial scales(from local to global)and biomes(temperate and alpine grasslands,forests and drylands).We revisited three methods to quantify multifunctionality including the averaging approach,summing approach and threshold-based approach.Important Findings Biodiversity–multifunctionality relationships either did not change or increased as more functions were considered.These results were best explained by the statistical underpinnings of the averaging and summing multifunctionality metrics.Specifically,by averaging the individual ecosystem functions,the biodiversity–multifunctionality relationships equal the population mean of biodiversity-single function relationships,and thus will not change with the number of functions.Likewise,by summing the individual ecosystem functions,the strength of biodiversity–multifunctionality relationships increases as the number of functions increased.We proposed a scaling standardization method by converting the averaging or summing metrics into a scaling metric,which would make comparisons among different biodiversity studies.In addition,we showed that the range-relevant standardization can be applied to the threshold-based approach by solving for the mathematical artefact of the approach(i.e.the effects of biodiversity may artificially increase with the number of functions considered).Our study highlights different approaches yield different results and that it is essential to develop an understanding of the statistical underpinnings of different approaches.The standardization methods provide a prospective way of comparing biodiversity–multifunctionality relationships across studies.

Linking discrete particle simulation to continuum process modelling for granular matter: Theory and application

Two approaches are widely used to describe particle systems： the continuum approach at macroscopic scale and the discrete approach at particle scale. Each has its own advantages and disadvantages in the modelling of particle systems. It is of paramount significance to develop a theory to overcome the disadvantages of the two approaches. Averaging method to link the discrete to continuum approach is a potential technique to develop such a theory. This paper introduces an averaging method, including the theory and its application to the particle flow in a hopper and the particle-fluid flow in an ironmaking blast furnace.

Determining Potential Passive Islanding Detection Indicators for Single-point Single Inverter,Single-point Multi-inverter and Multi-point Multi-inverter Scenarios

Distributed Generation(DG)sources,predominantly renewable energy-based,such as solar photovoltaic and wind energy sources,have significantly penetrated into power system networks.This high penetration of DG sources may lead to the formation of unintentional islands,which is hazardous to both the equipment and personnel,if sustained.In this paper,46 passive parameters are considered to find out which candidate(s)are promising for detecting sustained unintentional islands and avoid false DG trips.These 46 parameters are derived from point of common coupling(PCC)voltage,DG output current,frequency,power factor angle,active and reactive powers.All these parameters are tested on standard IEEE 13 and 34 bus distribution networks,integrated with inverter-interfaced DGs at different locations for different penetration levels in the MATLAB/SIMULINK environment.The parameters are tested for different islanding events(comprising of various local loads,such as conventional parallel RLC resonant load,R,RC,and RL loads)and for different non-islanding events.The parameters are then ranked accordingly by a suitable averaging approach based performance ranking technique.From this analysis,the best candidates are obtained for detecting inverter DG islands at single-point(or single PCC)locations and multi-point(or multiple PCCs)locations.Multiple best passive candidates are obtained for different island scenarios from which a set of promising islanding detection indicators are proposed.