Search results for "Exponent"

showing 10 items of 896 documents

An LMI approach to vibration control of base-isolated building structures with delayed measurements

2010

In this article, we address a convex optimisation approach to the problem of state-feedback H∞ control design for vibration reduction of base-isolated building structures with delayed measurements, where the delays are time-varying and bounded. An appropriate Lyapunov-Krasovskii functional and some free-weighting matrices are utilised to establish some delay-range-dependent sufficient conditions for the design of desired controllers in terms of linear matrix inequalities. The controller, which guarantees asymptotic stability and an H∞ performance, simultaneously, for the closed-loop system of the structure, is then developed. The performance of the controller is evaluated by means of simula…

Lyapunov functionEngineeringbusiness.industryVibration controlLinear matrix inequalityControl engineeringComputer Science ApplicationsTheoretical Computer Sciencesymbols.namesakeH-infinity methods in control theoryVibration isolationExponential stabilityControl and Systems EngineeringControl theorysymbolsbusinessReduction (mathematics)International Journal of Systems Science
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Stability analysis and H∞ controller synthesis of discrete-time switched systems with time delay

2014

Abstract This paper studies the problems of stability analysis and H ∞ controller synthesis of switched systems with time-varying delay based on an input–output approach. The attention is focused on developing a new method to further reduce the conservatism of the existing results. The system under consideration is transformed into an interconnection system, and the scaled small gain condition for the interconnection systems is introduced. Based on the system transformation and the scaled small gain theorem, an improved delay-dependent stability criterion is proposed such that the interconnection system is asymptotically stable, which is also proved to guarantee the asymptotic stability of …

Lyapunov functionGeneral Computer ScienceStability criterionMechanical Engineeringsymbols.namesakeSmall-gain theoremDiscrete time and continuous timeExponential stabilityControl and Systems EngineeringControl theoryStability theoryConvex optimizationsymbolsElectrical and Electronic EngineeringMathematicsSystems & Control Letters
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Study of irregular dynamics in an economic model: attractor localization and Lyapunov exponents

2021

Cyclicity and instability inherent in the economy can manifest themselves in irregular fluctuations, including chaotic ones, which significantly reduces the accuracy of forecasting the dynamics of the economic system in the long run. We focus on an approach, associated with the identification of a deterministic endogenous mechanism of irregular fluctuations in the economy. Using of a mid-size firm model as an example, we demonstrate the use of effective analytical and numerical procedures for calculating the quantitative characteristics of its irregular limiting dynamics based on Lyapunov exponents, such as dimension and entropy. We use an analytical approach for localization of a global at…

Lyapunov functionGeneral MathematicsChaoticFOS: Physical sciencesGeneral Physics and AstronomyattraktoritAbsorbing set (random dynamical systems)Lyapunov exponentInstabilitysymbols.namesakeDimension (vector space)AttractorApplied mathematicsEntropy (information theory)taloudelliset mallitdynaamiset systeemitMathematicskaaosteoriaApplied MathematicsLyapunov exponentstaloudelliset ennusteetkausivaihtelutStatistical and Nonlinear PhysicsAbsorbing setNonlinear Sciences - Chaotic DynamicsNonlinear Sciences::Chaotic DynamicsMid-size firm modelLyapunov dimensionsymbolsUnstable periodic orbitChaotic Dynamics (nlin.CD)Chaos, Solitons & Fractals
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Perturbation of the Lyapunov spectra of periodic orbits

2012

We describe all Lyapunov spectra that can be obtained by perturbing the derivatives along periodic orbits of a diffeomorphism. The description is expressed in terms of the finest dominated splitting and Lyapunov exponents that appear in the limit of a sequence of periodic orbits, and involves the majorization partial order. Among the applications, we give a simple criterion for the occurrence of universal dynamics.

Lyapunov functionGeneral MathematicsMathematical analysisPerturbation (astronomy)Dynamical Systems (math.DS)Lyapunov exponentSpectral linesymbols.namesakeFOS: MathematicssymbolsLimit of a sequencePeriodic orbitsDiffeomorphismMathematics - Dynamical SystemsMajorizationMathematicsProceedings of the London Mathematical Society
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Numerical analysis of dynamical systems: unstable periodic orbits, hidden transient chaotic sets, hidden attractors, and finite-time Lyapunov dimensi…

2018

In this article, on the example of the known low-order dynamical models, namely Lorenz, Rossler and Vallis systems, the difficulties of reliable numerical analysis of chaotic dynamical systems are discussed. For the Lorenz system, the problems of existence of hidden chaotic attractors and hidden transient chaotic sets and their numerical investigation are considered. The problems of the numerical characterization of a chaotic attractor by calculating finite-time time Lyapunov exponents and finite-time Lyapunov dimension along one trajectory are demonstrated using the example of computing unstable periodic orbits in the Rossler system. Using the example of the Vallis system describing the El…

Lyapunov functionHistoryMathematics::Dynamical SystemsDynamical systems theoryNumerical analysisChaoticFOS: Physical sciencesLyapunov exponentLorenz systemNonlinear Sciences - Chaotic DynamicsComputer Science ApplicationsEducationNonlinear Sciences::Chaotic Dynamicssymbols.namesakeAttractorsymbolsTrajectoryApplied mathematicsChaotic Dynamics (nlin.CD)Mathematics
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Exponential Transients in Continuous-Time Symmetric Hopfield Nets

2001

We establish a fundamental result in the theory of continuous-time neural computation, by showing that so called continuous-time symmetric Hopfield nets, whose asymptotic convergence is always guaranteed by the existence of a Liapunov function may, in the worst case, possess a transient period that is exponential in the network size. The result stands in contrast to e.g. the use of such network models in combinatorial optimization applications. peerReviewed

Lyapunov functionHopfield netsstabilityneural networksExponential functionHopfield networksymbols.namesakeModels of neural computationRecurrent neural networkConvergence (routing)symbolsApplied mathematicsCombinatorial optimizationdynaamiset systeemitAlgorithmMathematicsNetwork model
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Local Capacity $H_{\infty}$ Control for Production Networks of Autonomous Work Systems With Time-Varying Delays

2010

This paper considers the problem of local capacity H∞ control for a class of production networks of autonomous work systems with time-varying delays in the capacity changes. The system under consideration is modeled in a discrete-time singular form. Attention is focused on the design of a controller gain for the local capacity adjustments which maintains the work-in-progress (WIP) in each work system in the vicinity of planned levels and guarantees the asymptotic stability of the system and reduces the effect of the disturbance input on the controlled output to a prescribed level. In terms of a matrix inequality, a sufficient condition for the solvability of this problem is presented using …

Lyapunov functionInput/outputdelayAutonomous systems; delay; linear matrix inequality (LMI); production networks; Control and Systems Engineering; Electrical and Electronic EngineeringLinear matrix inequalityAutonomous systemssymbols.namesakeExponential stabilityDiscrete time and continuous timeControl and Systems EngineeringControl theoryConvex optimizationsymbolsproduction networksAutomatic gain controlSymmetric matrixElectrical and Electronic Engineeringlinear matrix inequality (LMI)MathematicsIEEE Transactions on Automation Science and Engineering
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A new fuzzy robust dynamic controller for autonomous vehicles with nonholonomic constraints

2005

Abstract In this paper a novel algorithm with a dynamic fuzzy controller applied to the control of trajectory of vehicles with two independent wheels is proposed. An automatic control of trajectory of a vehicle can behave in a not efficient way. It is necessary to consider the friction of the actuators and possible perturbations coming from the outside environment, as for instance the variable characteristics of the ground where the vehicle moves. These perturbations, which depend also on the contact between the wheel and the ground, involve violations of nonholonomic constraints. Thus it is necessary to compensate for these perturbations to obtain a robust control system. The controller sy…

Lyapunov functionMathematical optimizationAdaptive controlAutomatic controlComputer scienceGeneral MathematicsFuzzy logicComputer Science::Roboticssymbols.namesakeExponential stabilityControl theoryNonholonomic systemAdaptive neuro fuzzy inference systembackstepping controlautonomous vehicleFuzzy control systemComputer Science Applicationsnonholonomic systemFuzzy controllerControl and Systems EngineeringBacksteppingsymbolsTrajectoryRobust controlActuatorrobust controlSoftwareRobotics and Autonomous Systems
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Robust control of continuous-time systems with state-dependent uncertainties and its application to electronic circuits

2014

In this paper, the problems of robust stability and stabilization are investigated for a class of continuous-time uncertain systems. The uncertainties in the model are state-dependent and belong to a polytopic convex set, as can be found in many electronic circuits and some other applications. The global asymptotic stability conditions for such systems are first established by the classic common quadratic Lyapunov function approach. To reduce conservativeness, a particular class of nonquadratic parameter-dependent Lyapunov functions is introduced, by which improved robust stability conditions for the underlying systems are also derived. Based on the stability criteria, a static output feedb…

Lyapunov functionMathematical optimizationConvex setStability (learning theory)robust stabilitysymbols.namesakevectorsExponential stabilityControl theoryElectronic circuitsElectrical and Electronic EngineeringuncertaintyLyapunov methodsMathematicsLyapunov functionsComputer Science Applications1707 Computer Vision and Pattern RecognitionStability conditionsuncertain systemsControl and Systems Engineeringsymbolselectronic circuitsElectronic circuits; Lyapunov functions; polytopic uncertainties; robust stability; Control and Systems Engineering; Computer Science Applications1707 Computer Vision and Pattern Recognition; Electrical and Electronic EngineeringRobust controlrobust controlNetwork analysispolytopic uncertainties
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Local capacity H<inf>∞</inf> control for production networks of autonomous work systems with time-varying delays

2009

This paper considers the problem of local capacity H ∞ control for a class of production networks of autonomous work systems with time-varying delays in the capacity changes. The system under consideration is modelled in a discrete-time singular form. Attention is focused on the design of a controller gain for the local capacity adjustments which maintains the work in progress (WIP) in each work system in the vicinity of planned levels and guarantees the asymptotic stability of the system and reduces the effect of the disturbance input on the controlled output to a prescribed level. In terms of a matrix inequality, a sufficient condition for the solvability of this problem is presented usin…

Lyapunov functionMathematical optimizationWork in processsymbols.namesakeMatrix (mathematics)Exponential stabilityControl theoryConvex optimizationsymbolsProduction (economics)Work systemsMATLABcomputerMathematicscomputer.programming_language2009 European Control Conference (ECC)
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