Search results for "Lyapunov equation"

showing 6 items of 6 documents

Analytic Exact Upper Bound for the Lyapunov Dimension of the Shimizu–Morioka System

2015

In applied investigations, the invariance of the Lyapunov dimension under a diffeomorphism is often used. However, in the case of irregular linearization, this fact was not strictly considered in the classical works. In the present work, the invariance of the Lyapunov dimension under diffeomorphism is demonstrated in the general case. This fact is used to obtain the analytic exact upper bound of the Lyapunov dimension of an attractor of the Shimizu–Morioka system. peerReviewed

Lyapunov functionPure mathematicsMathematics::Dynamical SystemsGeneral Physics and Astronomylcsh:AstrophysicsLyapunov exponentUpper and lower boundssymbols.namesakeShimizu-Morioka systemDimension (vector space)Attractorlcsh:QB460-466Lyapunov equationLyapunov redesignlcsh:ScienceMathematicsta111Mathematical analysisShimizu–Morioka systemlcsh:QC1-999Nonlinear Sciences::Chaotic DynamicssymbolsLyapunov dimensionlcsh:QDiffeomorphismLyapunov exponentlcsh:PhysicsEntropy
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Analysis of singular bilinear systems using Walsh functions

1991

The use of Walsh functions to analyse singular bilinear systems is investigated. It is shown that the nonlinear implicit differential system equation may be converted to a set of linear algebraic Lyapunov equations to be solved iteratively for the coefficients of the semistate x(t) in terms of the Walsh basis functions. Solution of the iterative algorithm is uniformly convergent to the exact solution of the algebraic generalised Lyapunov equation of the singular bilinear system. The present method is slightly more complicated than a similar one arising from the analysis of linear singular systems. In fact, it is a hybrid between the analyses of usual linear singular and bilinear regular sys…

Lyapunov functionRegular singular pointMathematical analysisGeneral EngineeringBilinear interpolationBilinear formsymbols.namesakeSingular solutionWalsh functionsymbolsApplied mathematicsLyapunov equationMathematicsSingular point of an algebraic varietyIEE Proceedings D Control Theory and Applications
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Sampled-Data Control of Spacecraft Rendezvous with Discontinuous Lyapunov Approach

2013

Published version of an article in the journal: Mathematical Problems in Engineering. Also available from the publisher at: http://dx.doi.org/10.1155/2013/814271 Open Access This paper investigates the sampled-data stabilization problem of spacecraft relative positional holding with improved Lyapunov function approach. The classical Clohessy-Wiltshire equation is adopted to describe the relative dynamic model. The relative position holding problem is converted into an output tracking control problem using sampling signals. A time-dependent discontinuous Lyapunov functionals approach is developed, which will lead to essentially less conservative results for the stability analysis and control…

Lyapunov functionSpacecraftArticle Subjectbusiness.industryGeneral Mathematicslcsh:MathematicsGeneral EngineeringSampling (statistics)lcsh:QA1-939Stability (probability)symbols.namesakeExponential stabilityControl theoryPosition (vector)lcsh:TA1-2040symbolsLyapunov equationVDP::Matematikk og Naturvitenskap: 400::Matematikk: 410::Anvendt matematikk: 413businesslcsh:Engineering (General). Civil engineering (General)MathematicsMathematical Problems in Engineering
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Novel Stability Criteria for T--S Fuzzy Systems

2014

In this paper, novel stability conditions for Takagi-Sugeno (T-S) fuzzy systems are presented. The so-called nonquadratic membership-dependent Lyapunov function is first proposed, which is formulated in a higher order form of both the system states and the normalized membership functions than existing techniques in the literature. Then, new membership-dependent stability conditions are developed by the new Lyapunov function approach. It is shown that the conservativeness of the obtained criteria can be further reduced as the degree of the Lyapunov function increases. Two numerical examples are given to demonstrate the effectiveness and less conservativeness of the obtained theoretical resul…

Lyapunov functionpolynomialsFuzzy setStability (learning theory)Lyapunov function; membership-dependent; stability; Takagi-Sugeno (T-S) fuzzy system; Control and Systems Engineering; Computational Theory and Mathematics; Artificial Intelligence; Applied Mathematicssymbols.namesakevectorsTakagi-Sugeno (T-S) fuzzy systemComputer Science::Systems and ControlArtificial IntelligenceControl theoryLyapunov equationLyapunov redesignLyapunov methodsMathematicsLyapunov functionDegree (graph theory)membership-dependentstability criteriaApplied Mathematicseducational institutionsFuzzy control systemstabilityStability conditionsComputational Theory and MathematicsControl and Systems Engineeringfuzzy systemssymbolsIEEE Transactions on Fuzzy Systems
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Lyapunov Functions for Second-Order Differential Inclusions: A Viability Approach

2001

AbstractIn this paper the existence of Lyapunov functions for second-order differential inclusions is analyzed by using the methodology of the Viability Theory. A necessary assumption on the initial states and sufficient conditions for the existence of local and global Lyapunov functions are obtained. An application is also provided.

Lyapunov functionsecond orderViability theoryApplied MathematicsMathematical analysisOrder (ring theory)Lyapunov exponentExponential functionsymbols.namesakeDifferential inclusiondifferential inclusionssymbolsLyapunov equationviability theoryExponential decayAnalysisMathematicsLyapunov functionsJournal of Mathematical Analysis and Applications
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H<inf>∞</inf> controller design for the synchronization of a hyper-chaotic system

2013

In this paper, the robust control on the synchronization of a hyper-chaotic system is investigated. Based on Lyapunov stability theory and linear matrix inequality techniques, the multi-dimensional and the single-dimensional robust H∞ synchronization controllers are constructed for the possible application in practical engineering. Some numerical simulations are provided to demonstrate the effectiveness of the presented controllers.

Lyapunov stabilitysymbols.namesakeControl theoryChaoticsymbolsLinear matrix inequalityControl engineeringLyapunov equationLyapunov exponentRobust controlLyapunov redesignSynchronizationMathematics2013 9th Asian Control Conference (ASCC)
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