Stability of time-varying systems in the absence of strict Lyapunov functions

When a non-linear system has a strict Lyapunov function, its stability can be studied using standard tools from Lyapunov stability theory. What happens when the strict condition fails? This paper provides an answer to that question using a formulation that does not make use of the specific structure of the system model. This formulation is then applied to the study of the asymptotic stability of some classes of linear and non-linear time-varying systems.Peer ReviewedPostprint (author's final draft

Impact of Stratigraphic and Sedimentological Heterogeneity on Hydrocarbon Recovery in Carbonate Reservoirs

Imperial Users onl

Analysis and Design of Adaptive OCDMA Passive Optical Networks

OCDMA systems can support multiple classes of service by differentiating code parameters, power level and diversity order. In this paper, we analyze BER performance of a multi-class 1D/2D OCDMA system and propose a new approximation method that can be used to generate accurate estimation of system BER using a simple mathematical form. The proposed approximation provides insight into proper system level analysis, system level design and sensitivity of system performance to the factors such as code parameters, power level and diversity order. Considering code design, code cardinality and system performance constraints, two design problems are defined and their optimal solutions are provided. We then propose an adaptive OCDMA-PON that adaptively shares unused resources of inactive users among active ones to improve upstream system performance. Using the approximated BER expression and defined design problems, two adaptive code allocation algorithms for the adaptive OCDMA-PON are presented and their performances are evaluated by simulation. Simulation results show that the adaptive code allocation algorithms can increase average transmission rate or decrease average optical power consumption of ONUs for dynamic traffic patterns. According to the simulation results, for an adaptive OCDMA-PON with BER value of 1e-7 and user activity probability of 0.5, transmission rate (optical power consumption) can be increased (decreased) by a factor of 2.25 (0.27) compared to fixed code assignment.Comment: 11 pages, 11 figure

Quantitative genetics of maize (Zea mays L.) during seedling establishment under cool conditions : a thesis presented in partial fulfillment of the requirements for the degree of Master of Agricultural Science in Plant Science at Massey University

Two experiments were conducted to study cool tolerance in maize (Zea mays L.). The first experiment was carried out under controlled environment to evaluate several genotypes from five synthetic populations which are currently being used to develop hybrid maize for better adaptation to New Zealand climate and to study the qualitative inheritance of maize seedling growth under cool conditions. In this study, diurnal temperature of 16 °C day/6 °C night was used and characters related to seedling growth were examined. The second experiment conducted to study the effect of temperature on maize during its early growth and to examine whether the initial seed constitution and germination characteristics could be used as selection criteria for improvement of the subsequent seedling growth. Eleven physical, chemical, and morphological characters were measured. The growth was studied in germinators under two temperature regimes of 25/20 and 16/6 °C. The genotypic variation was highly significant for all nine characters examined in the first experiment. For the three repeatedly measured characters (i.e. chlorophyll content, shoot and root dry masses), the genotype x time interaction effect was significant. In the second experiment, the variation due to genotypic difference was highly significant only for the initial seed constitution characters and the amount of ion leakage during the early hours of germination process. It was non significant for the time to germinate, seedling growth rates, and seedling growth functions. The variation due to the difference of temperature regimes was significant for the time to germinate and seedling growth but not the growth functions. The genotypes of synthetic line NZS3 showed the best performance for general combining ability (GCA) for almost all characters studied in the first experiment. From all genotypes evaluated, however, only few of them consistently showed good GCA over the characters. Four of the characters studied in the first experiment had moderate to high narrow sense heritabilities, namely total leaves at 50 days after planting (82 %), chlorophyll content (46 %), anthocyanin (69%), and leaf area (62 %). In the second experiment, the estimated broad sense heritabilities observed ranged from very low to very high over all characters. The high broad sense heritabilities were recorded on most of the initial seed constitution characters, the conductivity of ion leakage, and the growth rates of root (length) and shoot (dry mass). Both the phenotypic and genotypic correlation coefficients between pairs are in good agreement and followed the same direction. Amongst the characters examined in the first experiment only time to achieve second mature leaf, total leaf number at 50 day after planting, chlorophyll content, leaf area had considerable correlations to the dry masses. In the second experiment a good correlation with growth rate was observed for the seed weight, nitrogen and maltose contents