KGmax Curves Associated With Second Generation Intact Stability Criteria for Different Types of Ships

Currently, second generation intact stability criteria are being developed and evaluated by the International Maritime Organization(IMO). In this paper, we briefly present levels 1 and 2 assessment methods for the criteria of pure loss of stability and parametric roll failure modes. Subsequently, we show the KG_(max) curves associated with these criteria. We compute these curves for five different types of ships and compare them with the curves embodied in the current regulations. The results show that the safety margin ensured by the first level-1 method of calculation for both pure loss of stability and parametric roll seems to be excessive in many cases. They also show that the KG_(max) given by the second level-1 method and by the level-2 method may be very similar. In some cases, the level-2 method can be more conservative than the second level-1 method, which is unanticipated by the future regulation. The KG_(max) curves associated with parametric roll confirm that the C11 container ship is vulnerable to this failure mode. The computation of the second check coefficient of parametric roll level 2(C2) for all possible values of KG reveals the existence of both authorized and restricted areas on the surface formed by both the draft and KG, which may replace the classical KG_(max) curves. In consequence, it is not sufficient to check that C2 is lower than the maximum authorized value(R_(PR0)) for a fixed ship's loading condition.

Delay-dependent criteria for the robust stability of systems with time-varying delay

The problem of delay-dependent robust stability for systems with time-varying delay has been considered. By using the S-procedure and the Park's inequality in the recent issue, a delay-dependent robust stability criterion which is less conservative than the previous results has been derived for time-delay systems with time-varying structured uncertainties. The same idea has also been easily extended to the systems with nonlinear perturbations. Numerical examples illustrated the effectiveness and the improvement of the proposed approach. Keywords Delay-dependent criteria - Robust stability - Time-varying structured uncertainties - Nonlinear perturbations - Linear matrix inequality This work was supported by the Doctor Subject Foundation of China (No. 2000053303).

Delay-dependent Criteria for Robust Stability of Uncertain Switched Hopfield Neural Networks

This paper deals with the problem of delay-dependent robust stability for a class of switched Hopfield neural networks with time-varying structured uncertainties and time-varying delay. Some Lyapunov-KrasoVskii functionals are constructed and the linear matrix inequality （LMI） approach and free weighting matrix method are employed to devise some delay-dependent stability criteria which guarantee the existence, uniqueness and global exponential stability of the equilibrium point for all admissible parametric uncertainties. By using Leibniz-Newton formula, free weighting matrices are employed to express this relationship, which implies that the new criteria are less conservative than existing ones. Some examples suggest that the proposed criteria are effective and are an improvement over previous ones.

Delay-dependent exponential stability criteria for stochastic systems with polytopic-type uncertainties

This paper considers the problem of delay-dependent exponential stability in mean square for stochastic systems with polytopic-type uncertainties and time-varying delay. Applying the descriptor model transformation and introducing free weighting matrices, a new type of Lyapunov-Krasovskii functional is constructed based on linear matrix inequalities （LMIs）, and some new delay-dependent criteria are obtained. These criteria include the delay-independent/rate- dependent and delay-dependent/rate-independent exponential stability criteria. These new criteria are less conservative than existing ones. Numerical examples demonstrate that these new criteria are effective and are an improvement over existing ones.

NECESSARY AND SUFFICIENT CRITERIA FOR ABSOLUTE STABILITY OF THE DIRECT CONTROL SYSTEM

Some necessary and sufficient conditions for absolute stability of several classes of direct control system were given, and two simplified forms of the control systems obtained twice were discussed. The results improve those of previous works.

An assessment of coal pillar system stability criteria based on a mechanistic evaluation of the interaction between coal pillars and the overburden

Coal pillar design has historically assigned a factor of safety(Fo S) or stability factor(SF) according to their estimated strength and the assumed overburden load acting on them. Acceptable Fo S values have been assigned based on past mining experience or a statistical link between Fo S and probability of failure(Po F). Pillar width-to-height(w/h) ratio has long been established as having a material influence on both pillar strength and its potential failure mode. However, there has been significant disagreement on using both factor of safety(Fo S) and w/h as part of pillar system stability criterion, as compared to using Fo S in isolation. This paper will argue that there are valid technical reasons to bring w/h ratio into system stability criteria(other than its influence on pillar strength), as it is related to the post-failure stiffness of the pillar, as measured in situ, and its interaction with overburden stiffness. When overburden stiffness is also brought into pillar system stability considerations, two issues emerge. The first is the width-todepth(W/D) ratio of the panel and whether it is sub-critical or super-critical from a surface subsidence perspective. The second relates to a re-evaluation of pillar Fo S based on whether the pillar is in an elastic or non-elastic(i.e., post-yield) state in its as-designed condition, as this is relevant to maintaining overburden stiffness at the highest possible level. The significance of the model is the potential to maximise both reserve recovery and mining efficiencies without any discernible increase in geotechnical risk, particularly in thick seams and higher depth of cover mining situations. At a time when mining economics are, at best, marginal, removing potentially unnecessary design conservatism is of interest to all mine operators and is an important topic for discussion amongst the geotechnical community.

Improved delay-dependent stability criteria for systems with interval delay

This paper deals with the problem of stability for systems with delay varying in an interval.A new Lyapunov functional,which makes use of the information of both the lower and upper bounds of the interval time-varying delay,is proposed to derive some new stability criteria.Furthermore,the relationship of the time-varying delay and its lower bound and upper bound is taken into account.As a result,some less conservative delay-dependent stability criteria are obtained without ignoring any useful information in the derivative of Lyapunov functional,which are established in the forms of linear matrix inequalities.Numerical examples are provided to show that the obtained results are better than existing ones.

Optimal control approach to stability criteria on Hill's equations

This paper gives a tutorial on how to prove Lyapunov type criteria by optimal control methods. Firstly, we consider stability criteria on Hill’s equations with nonnegative potential. By optimal control methods developed in 1990s, we obtain several stability criteria including Lyapunov’s criterion, Neǐgauz and Lidskiǐ’s criterion. Secondly, we present stability criteria on Hill’s equations with sign-changing potential in which Brog’s criterion and Krein’s criterion are included.

Stability criteria for linear systems with multiple time-varying delays

New delay-independent and delay-dependent stability criteria for linear systems with multiple time-varying delays are established by using the time-domain method. The results are derived based on a new-type stability theorem for general retarded dynamical systems and new analysis techniques developed in the author's previous work. Unlike some results in the literature, all of the established results do not depend on the derivative of time-varying delays. Therefore, they are suitable for the case with very fast time-varying delays. In addition, some remarks are also given to explain the obtained results and to point out the limitations of the previous results in the literature. Keywords Stability - Delay-independent criteria - Delay-dependent criteria - Linear time-delay systems - Multiple time-varying delays This work was supported by NSFC Key-Project (No. 60334010) and Guangdong Province Natural Science Foundation of China (No. 31406).

Criteria for the Nonlinear Stability of Three-Dimensional Quasi-Geostrophic Motions

Some more proper criteria for the nonlinear stability of three-dimensional quasi-geostrophic motions are given by combining variational principle with a prior estimates method. The criteria are suitable for perturbations of initial condition as well as parameters in the model. The basic flow can be steady or unsteady. Particularly the difficulty due to the nonlinear boundary condition is completely overcome by the use of our method.

Stability Criteria to the Incompressible Inviscid Linear Fluid between Two Rotation Coaxial Cylinders

The stability and instability phenomenon coupled with the rotation effect and the thermal convection between two concentric cylinders was studied. By means of the Normal-Modes method, the stability or instability criteria for the linearized system in terms of the oscillation frequency, the axial wavelength and the background thermal gradient are proved. Besides, some numerical simulation for the axisymmetric perturbations is presented.

Criteria of Stability for a Class of Linear Systems

In this paper, employing the geometric criteria of stability we obtain some stable results of linear differential equations with impulsive effects.

On delay-dependent robust stability for uncertain neutral systems

The problem of delay-dependent criteria for the robust stability of neutral systems with time-varying structured uncertainties and identi-cal neutral-delay and discrete-delay is concerned. A criterion for nominal systems is presented by taking the relationship between the terms in the Leibniz-Newton formula into account, which is described by some free-weighting matrices. In addition, this criterion is extended to robust stability of the systems with time-varying structured uncertainties. All of the criteria are based on linear matrix inequality such that it is easy to calculate the upper bound of the time-delay and the free-weighting matrices. Numerical examples illustrate the effectiveness and the improvement over the existing results.

Robust stability analysis of singular linear system with delay and parameter uncertainty

This paper deals with the problem of robust stability for continuous-time singular systems with state delay and parameter uncertainty. The uncertain singular systems with delay considered in this paper are assumed to be regular and impulse free.By decomposing the systems into slow and fast subsystems,a robust delay-dependent asymptotic stability criteria based on linear matrix inequality is proposed, which is derived by using Lyapunov-Krasovskii functionals, neither model transformation nor bounding for cross terms is required in the derivation of our delay-dependent result. The robust delay-dependent stability criterion proposed in this paper is a sufficient condition. Finally, numerical examples and Matlab simulation are provided to illustrate the effectiveness of the proposed method.

On delay-dependent robust stability of neutral systems

The delay-dependent robust stability of uncertain linear neutral systems with delays is investigated. Both discrete-delay-dependent/neutral-delay-independent and neutral-/discrete- delay-dependent stability criteria will be developed. The proposed stability criteria are formulated in the form of linear matrix inequalities and it is easy to check the robust stability of the considered systems. By introducing certain Lyapunov-Krasovskii functional the mathematical development of our result avoids model transformation and bounding for cross terms, which lead to conservatism. Finally, numerical example is given to indicate the improvement over some existing results.

Application of strength reduction method to dynamic anti-sliding stability analysis of high gravity dam with complex dam foundation

Considering that there are some limitations in analyzing the anti-sliding seismic stability of dam-foundation systems with the traditional pseudo-static method and response spectrum method, the dynamic strength reduction method was used to study the deep anti-sliding stability of a high gravity dam with a complex dam foundation in response to strong earthquake-induced ground action. Based on static anti-sliding stability analysis of the dam foundation undertaken by decreasing the shear strength parameters of the rock mass in equal proportion, the seismic time history analysis was carried out. The proposed instability criterion for the dynamic strength reduction method was that the peak values of dynamic displacements and plastic strain energy change suddenly with the increase of the strength reduction factor. The elasto-plastic behavior of the dam foundation was idealized using the Drucker-Prager yield criterion based on the associated flow rule assumption. The result of elasto-plastic time history analysis of an overflow dam monolith based on the dynamic strength reduction method was compared with that of the dynamic linear elastic analysis, and the reliability of elasto-plastic time history analysis was confirmed. The results also show that the safety factors of the dam-foundation system in the static and dynamic cases are 3.25 and 3.0, respectively, and that the F2 fault has a significant influence on the anti-sliding stability of the high gravity dam. It is also concluded that the proposed instability criterion for the dynamic strength reduction method is feasible.

Novel method of gait switching in six-legged robot walking on continuous-nondifferentiable terrain by utilizing stability and interference criteria

Continuous-nondifferentiable terrains are extremely challenging for the environment adaption of six-legged robots. Previous researches have focused on gait planning methods to improve inherent ability of legged robots to walk over moderate terrains.However,most six-legged robots utilize relatively monotonic gait so that they still cannot well adapt tough terrains. As a result,the current legged robots easily get stuck and fall when encountering continuous-nondifferentiable terrains,such as stairs.Therefore,a method of gait switching is proposed so that six-legged robots can flexibly generate multiple gaits to adapt complex terrains. This study investigated the relationship between six-legged robot gait topologies and physical constraints,such as robot stability and robot-terrain interference. The proposed gait switcher can generate 0-6,1-5,2-4 and 3-3 gaits,which is instructed by the stability and interference criteria. Simulations and experiments were performed on a novel six-legged robot Hexa-XIII that succeeded climbing stairs over 45°. The effectiveness of the gait switching method is validated by the experiment results.

Delay-dependent robust stability for neutral systems with mixed discrete-and-neutral delays

This paper focuses on the problem of delay-dependent robust stability of neutral systems with different discrete-and-neutral delays and time-varying structured uncertainties. Some new criteria are presented, in which some free weighting matrices are used to express the relationships between the terms in the Leibniz-Newton formula. The criteria include the information on the size of both neutral-and-discrete delays. It is shown that the present results also include the results for identical discrete-and-neutral delays as special cases. A numerical example illustrates the improvement of the proposed methods over the previous methods and the influences between the discrete and neutral delays.

Asymptotic Stability Criteria for Singular Differential Nonlinear Systems with Time-Varying Delays

In this paper, the asymptotic stability for singular differential nonlinear systems with multiple time-varying delays is considered. The V-functional method for general singular differential delay system is investigated. The asymptotic stability criteria for singular differential nonlinear systems with multiple time-varying delays are derived based on V-functional method and some analytical techniques, which are described as matrix equations or matrix inequalities. The results obtained are computationally flexible and efficient.

Manipulating Interfacial Stability Via Absorption-Competition Mechanism for Long-Lifespan Zn Anode

The stability of Zn anode in various Znbased energy storage devices is the key problem to be solved.Herein,aromatic aldehyde additives are selected to modulate the interface reactions between the Zn anode and electrolyte.Through comprehensively considering electrochemical measurements,DFT calculations and FEA simulations,novel mechanisms of one kind of aromatic aldehyde,veratraldehyde in inhibiting Zn dendrite/by-products can be obtained.This additive prefers to absorb on the Zn surface than H_(2)O molecules and Zn^(2+),while competes with hydrogen evolution reaction and Zn plating/stripping proces s via redox reactions,thus preventing the decomposition of active H_(2)O near the interface and uncontrollable Zn dendrite growth via a synactic absorption-competition mechanism.As a result,Zn-Zn symmetric cells with the veratraldehyde additive realize an excellent cycling life of 3200 h under 1 mA cm^(-2)/1 mAh cm^(-2)and over 800 h even under 5 mA cm^(-2)/5 mAh cm^(-2).Moreover,Zn-Ti and Zn-MnO_(2)cells with the veratraldehyde additive both obtain elevated performance than that with pure ZnSO_(4)electrolyte.Finally,two more aromatic aldehyde additives are chosen to prove their universality in stabilizing Zn anodes.