Stability criteria for single pulse solutions of cw passive mode-locked lasers

The stability of the steady-state solutions of mode-locking of cw lasers by a fast saturable absorber is imvestigated. It is shown that the solutions are stable if the condition (Ps/Pa) = (2/3) (P0Pa) is satisfied, where (Ps/Pa) is the steady-state la ser power, (P0/Pa) is the power at mode-locking threshold, and Pa is the saturated power of the absorber.

Optimal reactive power dispatch based on voltage stability criteria in a large power system with AC/DC and FACTs devices

An algorithm for optimal allocation of reactive power in AC/DC system using FACTs devices, with an objective of improving the voltage profile and also voltage stability of the system has been presented. The technique attempts to utilize fully the reactive power sources in the system to improve the voltage stability and profile as well as meeting the reactive power requirements at the AC-DC terminals to facilitate the smooth operation of DC links. The method involves successive solution of steady-state power flows and optimization of reactive power control variables with Unified Power Flow Controller (UPFC) using linear programming technique. The proposed method has been tested on a real life equivalent 96-bus AC and a two terminal DC system under normal and contingency conditions.

Average variation L2-stability criteria for time-varying feedback systems-A unified approach

The problem of developing L2-stability criteria for feedback systems with a single time-varying gain, which impose average variation constraints on the gain is treated. A unified approach is presented which facilitates the development of such average variation criteria for both linear and nonlinear systems. The stability criteria derived here are shown to be more general than the existing results.

New delay-dependent stability criteria for uncertain neutral systems with mixed time-varying delays and nonlinear perturbations

The problem of stability analysis for a class of neutral systems with mixed time-varying neutral, discrete and distributed delays and nonlinear parameter perturbations is addressed. By introducing a novel Lyapunov-Krasovskii functional and combining the descriptor model transformation, the Leibniz-Newton formula, some free-weighting matrices, and a suitable change of variables, new sufficient conditions are established for the stability of the considered system, which are neutral-delay-dependent, discrete-delay-range dependent, and distributeddelay-dependent. The conditions are presented in terms of linear matrix inequalities (LMIs) and can be efficiently solved using convex programming techniques. Two numerical examples are given to illustrate the efficiency of the proposed method

Stability criteria for the contextual emergence of macrostates in neural networks

More than thirty years ago, Amari and colleagues proposed a statistical framework for identifying structurally stable macrostates of neural networks from observations of their microstates. We compare their stochastic stability criterion with a deterministic stability criterion based on the ergodic theory of dynamical systems, recently proposed for the scheme of contextual emergence and applied to particular inter-level relations in neuroscience. Stochastic and deterministic stability criteria for macrostates rely on macro-level contexts, which make them sensitive to differences between different macro-levels.

On the existence of two-dimensional Euler flows satisfying energy-Casimir stability criteria

The energy-Casimir stability method, also known as the Arnold stability method, has been widely used in fluid dynamical applications to derive sufficient conditions for nonlinear stability. The most commonly studied system is two-dimensional Euler flow. It is shown that the set of two-dimensional Euler flows satisfying the energy-Casimir stability criteria is empty for two important cases: (i) domains having the topology of the sphere, and (ii) simply-connected bounded domains with zero net vorticity. The results apply to both the first and the second of Arnold’s stability theorems. In the spirit of Andrews’ theorem, this puts a further limitation on the applicability of the method. © 2000 American Institute of Physics.

Stability criteria for unsupervised temporal association networks

A biologically realizable, unsupervised learning rule is described for the online extraction of object features, suitable for solving a range of object recognition tasks. Alterations to the basic learning rule are proposed which allow the rule to better suit the parameters of a given input space. One negative consequence of such modifications is the potential for learning instability. The criteria for such instability are modeled using digital filtering techniques and predicted regions of stability and instability tested. The result is a family of learning rules which can be tailored to the specific environment, improving both convergence times and accuracy over the standard learning rule, while simultaneously insuring learning stability.

L2-stability of nonstationary feedback systems: Frequency-domain criteria

A frequency-domain positivity condition is derived for linear time-varying operators in2and is used to develop2stability criteria for linear and nonlinear feedback systems. These criteria permit the use of a very general class of operators in2with nonstationary kernels, as multipliers. More specific results are obtained by using a first-order differential operator with a time-varying coefficient as multiplier. Finally, by employing periodic multipliers, improved stability criteria are derived for the nonlinear damped Mathieu equation with a forcing function.

Asymptotic stability for time-variant systems and observability: Uniform and nonuniform criteria

This paper presents some new criteria for uniform and nonuniform asymptotic stability of equilibria for time-variant differential equations and this within a Lyapunov approach. The stability criteria are formulated in terms of certain observability conditions with the output derived from the Lyapunov function. For some classes of systems, this system theoretic interpretation proves to be fruitful since - after establishing the invariance of observability under output injection - this enables us to check the stability criteria on a simpler system. This procedure is illustrated for some classical examples.

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.

Deformation and stability regression models for soil nail walls

Lateral displacement and global stability are the two main stability criteria for soil nail walls. Conventional design methods do not adequately address the deformation behaviour of soil nail walls, owing to the complexity involved in handling a large number of influencing factors. Consequently, limited methods of deformation estimates based on empirical relationships and in situ performance monitoring are available in the literature. It is therefore desirable that numerical techniques and statistical methods are used in order to gain a better insight into the deformation behaviour of soil nail walls. In the present study numerical experiments are conducted using a 2 4 factorial design method. Based on analysis of the maximum lateral deformation and factor-of-safety observations from the numerical experiments, regression models for maximum lateral deformation and factor-of-safety prediction are developed and checked for adequacy. Selection of suitable design factors for the 2 4 factorial design of numerical experiments enabled the use of the proposed regression models over a practical range of soil nail wall heights and in situ soil variability. It is evident from the model adequacy analyses and illustrative example that the proposed regression models provided a reasonably good estimate of the lateral deformation and global factor of safety of the soil nail walls.

A Comparative Study of Liapunov Stability Analyses of Flexible Damped Satellites

A literal Liapunov stability analysis of a spacecraft with flexible appendages often requires a division of the associated dynamic potential into as many dependent parts as the number of appendages. First part of this paper exposes the stringency in the stability criteria introduced by such a division and shows it to be removable by a “reunion policy.” The policy enjoins the analyst to piece together the sets of criteria for each part. Employing reunion the paper then compares four methods of the Liapunov stability analysis of hybrid dynamical systems illustrated by an inertially coupled, damped, gravity stabilized, elastic spacecraft with four gravity booms having tip masses and a damper rod, all skewed to the orbital plane. The four methods are the method of test density function, assumed modes, and two and one-integral coordinates. Superiority of one-integral coordinate approach is established here. The design plots demonstrate how elastic effects delimit the satellite boom length.

Ab initio investigation of the elasticity and stability of aluminium

On the basis of the pseudopotential plane-wave (PP-PW) method in combination with the local density functional theory (LDFT), complete stress-strain curves for the uniaxial loading and uniaxial deformation along the [001] and [111] directions, and the biaxial proportional extension along [010] and [001] for aluminium are obtained. During the uniaxial loading, certain general behaviours of the energy versus the stretch and the load versus the stretch are confirmed; in each case, there exist three special unstressed structures: f.c.c., b.c.c., and f.c.t. for [001]; f.c.c., s.c., and b.c.c. for [111]. Using stability criteria, we find that all of these states are unstable, and always occur together with shear instability, except the natural f.c.c. structure. A Pain transformation from the stable f.c.c. structure to the stable b.c.c. configuration cannot be obtained by uniaxial compression along any equivalent [001] and [111] direction. The tensile strengths are similar for the two directions. For the higher energy barrier of the [111] direction, the compressive strength is greater than that for the [001] direction. With increase in the ratio of the biaxial proportional extension, the stress and tensile strength increase; however, the critical strain does not change significantly. Our results add to the existing ab initio database for use in fitting and testing interatomic potentials.