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Topic: Initial stability

    Note: these results are not from the primary (high quality) database.

BIBO Stability BIBO stability requires that the output remain bounded for all time, for all initial conditions and inputs - not just for some specific initial condition and input. A BIBO (bounded-input bounded-output) stable system is a system for which the outputs will remain bounded for all time, for any finite initial condition and input. A continuous-time linear time-invariant system is BIBO stable if and only if all the poles of the system have real parts less than 0. academic.csuohio.edu /simond/linearsystems/stability/bibo   (236 words)

New Books Every scalar (vector) physical variable can change its value at any place and at any moment only by passing (elementwise) through all intermediate scalar (vector) values between the initial and the final scalar (vector) value and it has a unique instantaneous scalar (vector) value at any place and at any moment. Every scalar (vector) physical variable can change its value at any place and at any moment only by passing (elementwise) through all intermediate scalar (vector) values between the initial and the final scalar (vector) value. Every scalar (vector) physical variable can change its value only continuously in time at any place and at any moment and it has a unique instantaneous scalar (vector) value at any place and at any moment. www.truth-action.com /13pcup.html   (236 words)

Long Touring Single E 68 ... the first report! The greater the resistance of the hull, the greater the initial stability. A certain measure of initial stability allows relaxed paddling. However, if you find yourself broadside on to a breaking wave, you might welcome the ability to overcome final stability in a controlled manner, lay the boat into the wave with your weight on the paddle and thus prevent the crest from capsizing you! www.pouchboats.com /e68_report.html   (2215 words)

FRCtheory97.html There is a general difficulty in connecting an initial equilibrium to a relaxed state. Have also done linear and non-linear MHD stability analysis of the 2D equilibrium formed by merging. The choice of initial equilibrium is probably ill informed and leads to exceedingly complicated (ugly) intermediate dynamics. w3.pppl.gov /frc/FRCtheory97.html   (959 words)

PlanetMath: stable sorting algorithm Stability is a useful property when the total ordering relation is dependent upon initial position. Some examples of stable sorting algorithms are bubblesort and mergesort (although the stability of mergesort is dependent upon how it is implemented). Using a stable sorting algorithm means that sorting by ascending position for equal keys is built-in, and need not be implemented explicitly in the comparison operator. planetmath.org /encyclopedia/UnstableSortingAlgorithm.html   (959 words)

Lyapunov stability - Wikipedia, the free encyclopedia Lyapunov stability is applicable to only unforced (no control input) dynamical systems. Lyapunov's realisation was that stability can be proven without requiring knowledge of the true physical energy, providing a Lyapunov function can be found to satisfy the above constraints. If the parameter ε is positive, stability is asymptotic for en.wikipedia.org /wiki/Lyapunov_stability   (501 words)

FRBSF: Economic Letter - Should Central Banks Stabilize Prices? (08/11/2000) In contrast, under a policy of price stability, the Fed would need to bring the price level back down to its initial level--a temporary period of inflation would need to be followed by a deflation, a fall in prices. The major argument against pursuing price stability, as opposed to low inflation, is that overall economic instability might increase. The benefits of long-term price stability, however, would be offset if a policy of price stability increased the volatility of inflation and the real economy. www.frbsf.org /econrsrch/wklyltr/2000/el2000-24.html   (1955 words)

Nonlinear Control Abstracts In the spirit of the ``input-to-state stability'' philosophy, it requires the state and the input of the system to be bounded by a suitable function of the output and derivatives of the output, modulo a decaying term depending on initial conditions. This feedback is shown to guarantee global stability in at least $H^2$ norm, which by Sobolev's embedding theorem implies continuity in space and time of both the flow field and the control (as well as their convergence to the desired steady state). The controller is sampled-data, periodic and in the absence of disturbances it yields a dead-beat behavior. www.math.rutgers.edu /~sontag/NCA   (1955 words)

Glossary of Dynamical Systems Terms Asymptotic stability A fixed point is asymptotically stable if it is stable and nearby initial conditions tend to the fixed point in positive time. A limit cycle is orbitally asymptotically stable if the Floquet multipliers of the linearized system lie inside the unit circle with the exception of a multiplier with value 1. Often indicates that the new branch is stable. mrb.niddk.nih.gov /glossary/glossary.html   (1955 words)

The Seattle Times: Snohomish County News: Illegal clear-cut leaves slope-stability concerns The results were that the slope is stable," said John Sadler, the project manager for Terra Associates, which did initial site evaluations for the condominium project and was called back to reassess the slope after the clear-cutting. Replanting the slope, clear-cut by Triad Development last winter in violation of city building permits, is the first of many steps the company has taken to address the damage. The city and a geotechnical consultant for Triad say the slope is stable and would be even during a sustained earthquake. seattletimes.nwsource.com /html/snohomishcountynews/2001973132_trees07n.html   (709 words)

Lyapunov stability - Wikipedia, the free encyclopedia Lyapunov stability is applicable to only unforced (no control input) dynamical systems. It is used to study the behaviour of dynamical systems under initial perturbations around equilibrium points. Then V(x) is called a Lyapunov function candidate and the system is asymptotically stable in the sense of Lyapunov. en.wikipedia.org /wiki/Lyapunov_stability   (709 words)

Eduardo Sontag Publications on the Web In the spirit of the ``input-to-state stability'' philosophy, it requires the state and the input of the system to be bounded by a suitable function of the output and derivatives of the output, modulo a decaying term depending on initial conditions. We establish global asymptotic stability, and in particular no oscillations, if the rate of transcription is somewhat smaller than that assumed by Goldbeter, but, on the other hand, this stability persists even under arbitrary delays in the feedback loop. The main contribution of this work is to establish a complete equivalence between the input-output-to-state stability property and the existence of a certain type of smooth Lyapunov function. www.math.rutgers.edu /~sontag/papers.html   (709 words)

Dassault Falcon Aircraft / What's New / Falconer Online The concept of static stability can be defined as the initial tendency of an object to diverge from or return to a state of equilibrium after having been disturbed. By relaxing the margins of stability on the Falcon 7X, aerodynamicists were able to optimize the performance of the airplane within those margins. Fly-by-wire changes the rules slightly by permitting a state of "relaxed stability," which leaves room for the designer to reduce the size and weight of various aerodynamic surfaces, creating new efficiencies. www.falconjet.com /whatsnew/falconer_article.jsp?DOCNUM=31232&IDOCNUM=31229   (526 words)

iss-ejc.html On the Input-to-State Stability Property Eduardo D. Sontag\Lambda Department of Mathematics Rutgers University, New Brunswick, NJ 08903y Abstract The "input to state stability" (iss) property provides a natural framework in which to formulate notions of stability with respect to input perturbations. Stability is clear: for small x and z, trajectories coincide with those that would result if uniformity would hold globally on x (cf. Rm for which (6) is well-posed; that is, for each initial state x(0) there is an absolutely continuous solution, defined at least for small times, and any two such solutions coincide on their interval of existence. www.math.rutgers.edu /~sontag/iss-ejc.html   (7051 words)

Lyapunov stability theory If asymptotic stability holds for any initial condition, the equilibrium point is said to be globally asymptotically stable. Note that for linear networks, asymptotic stability and global asymptotic stability are equivalent, so the distinction between local and global stability is not necessary. There are several mathematical definitions of the term ``stability.'' The one due to Lyapunov is most useful here. hebb.mit.edu /courses/9.641/2000/lectures/lecture10.html   (499 words)

Molecular Dynamics Simulation of the Human U2B" Protein Complex with U2 snRNA Hairpin IV in Aqueous Solution -- Guo and Gmeiner 81 (2): 630 -- Biophysical Journal The trajectory is stable after the initial 750 ps of MD. The stability of the RNA/protein complex is derived not only from direct interactions between protein and RNA, but also from The structure of this bridging water molecule was remarkably stable during the trajectory. www.biophysj.org /cgi/content/full/81/2/630   (499 words)

USGS - Shear strength and slope stability at sites in the Caribbean National Forest and Coamo area, Puerto Rico Slope failures in the Caribbean National Forest appear to occur by initial tensile failure of saprolite materials at the crown, followed by shear failure along the slope. In-situ shear strength tests, used in conjunction with slope-stability analyses are used to determine factors of safety, and failure mechanisms in landslide-prone areas in Puerto Rico. This combination of factors usually provides more stable slopes in the Coamo area than in the National Forest. pr.water.usgs.gov /public/webb/bibliography/abstract101.html   (314 words)

Asymptotic Stability of the Optimal Filter with Respect toIts Initial Condition For the linear case, stability of the Riccati equation of Kalman filtering is used to derive almost sure asymptotic stability of linear filters for possibly non-Gaussian initial conditions. If the solution to the filtering equations, initialized with an incorrect prior distribution, approaches the true conditional distribution asymptotically in time, then the filter is said to be asymptotically stable with respect to perturbations of the initial condition. In the nonlinear case, asymptotic stability in a weak convergence sense is shown for filters of signal diffusions which converge in law to an invariant distribution. epubs.siam.org /sam-bin/dbq/article/25661   (192 words)

summary Initial results were presented of a nonlinear 3D code in cylindrical geometry for the stability studies of FRC, M3D-B. The code utilizes a MHD/particle representation in which background plasma is described by MHD equations and energetic ions are treated using particle simulations. Plans are to study the stability as a function of profiles, shape, and s as the energetic ion fraction increases, and for a fully kinetic ion description. Tilt stability is expected to occur when s < C Z/R_s, where C is an equilibrium dependent constant, Z is the half-height of the FRC, and R_s is the mid-plane radius of the separatrix. w3.pppl.gov /frc/FRCtheory98.html   (1516 words)

2001-4.html Key words: Cantilevered pipe; fluid conveyed, resisting medium (foundation), added mass; added stiffness; local stability; global stability, critical velocities. By using the latter, as well as by using the concept of the local and global stability of the pipe, the dependence of the critical follower force on the stiffness of the resisting medium is proved. The solution of this problem gives the initial conditions of the process immediately following the instantaneous process. www.imbm.bas.bg /imbm/jtam/2001-4.html   (1516 words)

No Title Add small Gaussian noise to the second equation and simulate trajectories around one of the stable equilibria, assuming the initial condition at the equilibrium point. Analyze the Jacobian matrix at the equilibrium points and determine which of the equilibrium points are asymptotically stable, which are not asymptotically stable but may be stable, if any, and which are unstable. Sketch or plot approximate trajectories of the system around the equilibria. bass.gmu.edu /ececourses/inft841/Exp1/Exp1.html   (1516 words)

Swing-leg retraction: a simple control model for stable running -- Seyfarth et al. 206 (15): 2547 -- Journal of Experimental Biology the stability of the spring-mass model is investigated. 3, an increased retraction speed leads to an enlarged attraction of the stable fixed points with respect to a given initial (e.g. In their investigation of the stability of spring-mass jeb.biologists.org /cgi/content/full/206/15/2547   (1516 words)

protocelt.htm Initial consonantal mutation is as natural as initial consonantal stability in tone and non-tonal languages with declension and conjugation. Kenneth Jackson has postulated that Welsh initial consonant mutation began at the end of the fifth century and was complete by the end of the sixth century. Initial consonantal mutation is an increase in complexity, which might have developed in these situations from the fusion of different languages, but did not. members.aol.com /IrishWord/protocelt.htm   (1516 words)

Economics In this explanation, however, the United States is represented not as an aspiring hegemonic state in the spirit of hegemonic stability theory, but as the representative of a transnational capitalist class. Economic theory alone does not explain the early rise of huge firms in the United States, and so Charles Pen-ow traces the initial political institutions that encouraged capitalists to shape the regulations that they had to live by. The central argument advanced in Chapter 4 is that a political economicanalysis of IPRs requires corresponding theories of the state, class, and capital as they operate in the global economy. wordtrade.com /themes/economics2.htm   (15040 words)

Testing for Coefficient Constancy in Random Walk Models with Particular Reference to the Initial Value Problem When this initial value is allowed to be random, it is shown that the test statistics are either exactly the same, or possess the same asymptotic distributions, as when the initial value is fixed. In particular, we explore the effects that different assumptions about the initial value of the random walk process have on the form and asymptotic distribution of the resulting test statistics. This article is concerned with Locally Best Invariant tests for coefficient stability in a univariate random walk coefficient regression model. ideas.repec.org /a/spr/empeco/v14y1989i2p105-12.html   (15040 words)

Prof Gebotys 8. Euler Method SECTION Initial Value Problem: Euler method (use of Taylor), local error, global error, stability. The equations now must be solved to plot voltage over initial time (when circuit is powered up to 100 ms later). The engineer has designed a nifty circuit to control a flat panel display. optimal.vlsi.uwaterloo.ca /NEW/ece204/204-8.htm   (15040 words)

ECE441 Stability with respect to input signals (BIBO stability) and with respect to the initial conditions (Ljapunov stablity), Routh-Hurwitz criterion, margin of stability. Design of controller structures by use of Nyquist diagrams. Design of lead/lag compensators and other controllers by use of Bode diagrams. www.ece.arizona.edu /~cellier/ece441.html   (248 words)

Numerical Calculation of Lyapunov Exponents -- from Mathematica Information Center Therefore, they can be used to analyze the stability of limits sets and to check sensitive dependence on initial conditions, that is, the presence of chaotic attractors. They measure the average rate of divergence or convergence of orbits starting from nearby initial points. The Lyapunov characteristic exponents play a crucial role in the description of the behavior of dynamical systems. library.wolfram.com /infocenter/Articles/2902   (248 words)

UK Nonlinear News: Issue 28 (May 2002) Sensitive Dependence on Initial Conditions: Chaos and Stochastic Processes (Bologna University, Italy) Modelling dolphin hydrodynamics: the numerical analysis and hydrodynamic stability of flow past compliant surfaces (University of Surrey) www.amsta.leeds.ac.uk /Applied/news.dir/issue28.dir   (248 words)

Stabilizing South Eastern Europe Although initial funding for the Stability Pact has been slow to arrive, the Regional Funding Conference for South Eastern Europe received more than $2.3 billion in pledges last March to finance "quick-start projects."2 This amount was surprisingly high, exceeding the fundraising target by one third. It’s purpose, summarized by Bodo Hombach, Stability Pact special coordinator, is to create "a democratic and unified Europe without political and economic divisions."1 It would accomplish this by bringing the countries of South Eastern Europe together with those in Western Europe, the United States, and their institutions. Conceptually, the Stability Pact is a tremendous victory for advocates of peacekeeping and conflict prevention. www.basicint.org /pubs/Notes/2000stabilizingsouth.htm   (1327 words)

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