Construction of Stability Multipliers with Prescribed Phase Characteristics: an Improved Value for $\sigma

For a feedback system consisting of a transfer function $G(s)$ in the forward path and a time-varying gain $n(t)(0 \leqq n(t) \leqq k)$ in the feedback loop, a stability multiplier $Z(s)$ has been constructed (and used to prove stability) by Freedman [2] such that $Z(s)(G(s) + {1 / K})$ and $Z(s - \sigma )(0 < \sigma < \sigma _ * )$ are strictly positive real, where $\sigma _ * $ can be computed from a knowledge of the phase-angle characteristic of $G(i\omega ) + {1 / k}$ and the time-varying gain $n(t)$ is restricted by $\sigma _ * $ by means of an integral inequality. In this note it is shown that an improved value for $\sigma _ * $ is possible by making some modifications in his derivation. ©1973 Society for Industrial and Applied Mathematics.

Effect of drying, storage temperature and air exposure on astaxanthin stability from Haematococcus pluvialis

Astaxanthin is a powerful antioxidant with various health benefits such as prevention of age-related macular degeneration and improvement of the immune system, liver and heart function. To improve the post-harvesting stability of astaxanthin used in food, feed and nutraceutical industries, the biomass of the high astaxanthin producing alga Haematococcus pluvialis was dried by spray- or freeze-drying and under vacuum or air at − 20 °C to 37 °C for 20 weeks. Freeze-drying led to 41 higher astaxanthin recovery compared to commonly-used spray-drying. Low storage temperature (− 20 °C, 4 °C) and vacuum-packing also showed higher astaxanthin stability with as little as 12.3 ± 3.1 degradation during 20 weeks of storage. Cost-benefit analysis showed that freeze-drying followed by vacuum-packed storage at − 20 °C can generate AUD600 higher profit compared to spray-drying from 100 kg H. pluvialis powder. Therefore, freeze-drying can be suggested as a mild and more profitable method for ensuring longer shelf life of astaxanthin from H. pluvialis.

Topological stability through tame retractions

A smooth map is said to be stable if small perturbations of the map only differ from the original one by a smooth change of coordinates. Smoothly stable maps are generic among the proper maps between given source and target manifolds when the source and target dimensions belong to the so-called nice dimensions, but outside this range of dimensions, smooth maps cannot generally be approximated by stable maps. This leads to the definition of topologically stable maps, where the smooth coordinate changes are replaced with homeomorphisms. The topologically stable maps are generic among proper maps for any dimensions of source and target. The purpose of this thesis is to investigate methods for proving topological stability by constructing extremely tame (E-tame) retractions onto the map in question from one of its smoothly stable unfoldings. In particular, we investigate how to use E-tame retractions from stable unfoldings to find topologically ministable unfoldings for certain weighted homogeneous maps or germs. Our first results are concerned with the construction of E-tame retractions and their relation to topological stability. We study how to construct the E-tame retractions from partial or local information, and these results form our toolbox for the main constructions. In the next chapter we study the group of right-left equivalences leaving a given multigerm f invariant, and show that when the multigerm is finitely determined, the group has a maximal compact subgroup and that the corresponding quotient is contractible. This means, essentially, that the group can be replaced with a compact Lie group of symmetries without much loss of information. We also show how to split the group into a product whose components only depend on the monogerm components of f. In the final chapter we investigate representatives of the E- and Z-series of singularities, discuss their instability and use our tools to construct E-tame retractions for some of them. The construction is based on describing the geometry of the set of points where the map is not smoothly stable, discovering that by using induction and our constructional tools, we already know how to construct local E-tame retractions along the set. The local solutions can then be glued together using our knowledge about the symmetry group of the local germs. We also discuss how to generalize our method to the whole E- and Z- series.

Preparation and thermal stability of trioxalatocobaltates of bivalent metals KM2+ [Co(C2O4)3]·xH2O

Trioxalatocobaltates of bivalent metals KM2+[Co(C2O4)3]·x H2O, with M2+ = Ba, Sr, Ca and Pb, have been prepared, characterized and their thermal behaviour studied. The compounds decompose to yield potassium carbonate, bivalent metal carbonate or oxide and cobalt oxide as final products. The formation of the final products of decomposition is influenced by the surrounding atmosphere. Bivalent metal cobaltites of the types KM2+CoO3 and M2+CoO3—x are not identified among the final products of decomposition. The study brings out the importance of the decomposition mode of the precursor in producing the desired end products.

An exponential stability criterion for certain nonlinear systems

Improved sufficient conditions are derived for the exponential stability of a nonlinear time varying feedback system having a time invariant blockG in the forward path and a nonlinear time varying gain ϕ(.)k(t) in the feedback path. φ(.) being an odd monotone nondecreasing function. The resulting bound on is less restrictive than earlier criteria.

Time-domain criteria for theL_{2}-stability of nonstationary feedback systems

Criteria for the L2-stability of linear and nonlinear time-varying feedback systems are given. These are conditions in the time domain involving the solution of certain associated matrix Riccati equations and permitting the use of a very general class of L2-operators as multipliers.

Stability of large flexible damped spacecraft modeled as elastic continua

Vibrational stability of a large flexible, structurally damped spacecraft subject to large rigid body rotations is analysed modelling the system as an elastic continuum. Using solution of rigid body attitude motion under torque free conditions and modal analysis, the vibrational equations are reduced to ordinary differential equations with time-varying coefficients. Stability analysis is carried out using Floquet theory and Sonin-Polya theorem. The cases of spinning and non-spinning spacecraft idealized as a flexible beam plate undergoing simple structural vibration are analysed in detail. The critical damping required for stabilization is shown to be a function of the spacecraft's inertia ratio and the level of disturbance.

Storage stability of solid rocket fuels. 2. Effect of oxidizer loadings

Ageing behaviour, leading to ballistic changes, has been studied as a function of oxidizer loading in polystyrene/ammonium perchlorate solid-propellants. The ageing studies were carried out at 100 °C in air. Change in burning rate decreased as the oxidizer loading increased from 75 to 80%. The change in thermal decomposition rates both at 230 and 260 °C also decreased as the oxidizer loading in the propellants increased. The shapes of the plots of the changes in burning rate and thermal decomposition rate (230 and 260 °C) at different storage times for different oxidizer-loaded propellants seem to be exactly similar. These results lead to the conclusion that the thermal decomposition of the propellant may be responsible for bringing about the ballistic changes during the ageing process. Infrared studies of the binder portion of the aged propellant indicate that peroxide formation takes place during the course of ageing and that peroxide formation for a particular storage time and temperature increases as the loading decreases.

L_{2}- stability of a class of nonstationary feedback systems with dynamical nonlinear subsystems

A class of feedback systems, consisting of dynamical non-linear subsystems which arise in many diverse control applications, is analyzed for L2-stability. It is shown that, although a transformation of these systems to the familiar Lur'e configuration does not seem to be possible, a one-to-one correspondence may be effected between the stability properties of these and the Lur'e systems. Interesting stability criteria are developed by exploiting this characteristic.

Construction of stability multipliers for non-linear feedback systems

This paper is concerned with the analysis of the absolute stability of a non-linear autonomous system which consists of a single non-linearity belonging to a particular class, in an otherwise linear feedback loop. It is motivated from the earlier Popovlike frequency-domain criteria using the ' multiplier ' eoncept and involves the construction of ' stability multipliers' with prescribed phase characteristics. A few computer-based methods by which this problem can be solved are indicated and it is shown that this constitutes a stop-by-step procedure for testing the stability properties of a given system.

An exponential stability criterion for certain nonlinear systems

Improved sufficient conditions are derived for the exponential stability of a nonlinear time varying feedback system having a time invariant blockG in the forward path and a nonlinear time varying gain ϕ(.)k(t) in the feedback path. φ(.) being an odd monotone nondecreasing function. The resulting bound on $$\left( {{{\frac{{dk}}{{dt}}} \mathord{\left/ {\vphantom {{\frac{{dk}}{{dt}}} k}} \right. \kern-\nulldelimiterspace} k}} \right)$$ is less restrictive than earlier criteria.

On the positivity and stability of non-stationary systems

The positivity of operators in Hilbert spaces is an important concept finding wide application in various branches of Mathematical System Theory. A frequency- domain condition that ensures the positivity of time-varying operators in L2 with a state-space description, is derived in this paper by using certain newly developed inequalities concerning the input-state relation of such operators. As an interesting application of these results, an L2 stability criterion for time-varying feedback systems consisting of a finite-sector non-linearity is also developed.