Search results for "Lyapunov redesign"

showing 5 items of 5 documents

Observer-based adaptive stabilization of a class of uncertain nonlinear systems

2014

In this paper, an adaptive output feedback stabilization method for a class of uncertain nonlinear systems is presented. Since this approach does not require any information about the bound of uncertainties, this information is not needed a priori and a mechanism for its estimation is exploited. The adaptation law is obtained using the Lyapunov direct method. Since all the states are not measurable, an observer is designed to estimate unmeasurable states for stabilization. Therefore, in the design procedure, first an observer is designed and then the control signal is constructed based on the estimated states and adaptation law with the σ-modification algorithm. The uniformly ultimately bou…

Lyapunov functionMathematical optimizationControl and OptimizationAdaptive controlObserver (quantum physics)Chaoticsymbols.namesakeNonlinear systemArtificial IntelligenceControl and Systems EngineeringControl theorysymbolsA priori and a posterioriLyapunov redesignAdaptation (computer science)MathematicsSystems Science & Control Engineering
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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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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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Impulsive control on the synchronization for a class of chaotic Systems

2014

In this paper, the impulsive control problem on the synchronization for a class of chaotic systems is discussed. Based on Lyapunov stability theory, the new impulsive synchronization strategy is presented to realize the chaos synchronization and possesses the wider scope of application. Finally the numerical simulation examples are given to demonstrate the effectiveness of our theoretical results.

Lyapunov stabilitychaos systemClass (set theory)Computer simulationSynchronization of chaoschaos system; impulsive switching; Lyapunov stability; synchronization; Electrical and Electronic Engineering; Control and Systems EngineeringLyapunov exponentimpulsive switchingSynchronizationNonlinear Sciences::Chaotic DynamicsCHAOS (operating system)symbols.namesakeControl and Systems EngineeringControl theoryLyapunov stabilitysymbolsElectrical and Electronic EngineeringLyapunov redesignsynchronizationMathematics2014 IEEE 23rd International Symposium on Industrial Electronics (ISIE)
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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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