Search results for "Lyapunov function"

showing 10 items of 104 documents

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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On integral input-to-state stability for a feedback interconnection of parameterised discrete-time systems

2014

This paper addresses integral input-to-state stability iISS for a feedback interconnection of parameterised discrete-time systems involving two subsystems. Particularly, we give a construction for a smooth iISS Lyapunov function for the whole system from the sum of nonlinearly weighted Lyapunov functions of individual subsystems. Motivations for such a construction are given. We consider two main cases. The first one investigates iISS for the whole system when both subsystems are iISS. The second one gives iISS for the interconnected system when one of subsystems is allowed to be input-to-state stable. The approach is also valid for both discrete-time cascades and a feedback interconnection…

Lyapunov functionsmall-gain conditions0209 industrial biotechnologyInterconnectionStability (learning theory)Computer Science Applications1707 Computer Vision and Pattern Recognition02 engineering and technologyState (functional analysis)Computer Science ApplicationsWhole systems0-global asymptotic stabilityTheoretical Computer Scienceinput-to-state stabilitysymbols.namesakeparameterised discrete-time systems020901 industrial engineering & automationDiscrete time and continuous timeControl theoryControl and Systems Engineering0202 electrical engineering electronic engineering information engineeringsymbols020201 artificial intelligence & image processing0-global asymptotic stability; input-to-state stability; integral input-to-state stability; parameterised discrete-time systems; small-gain conditions; Control and Systems Engineering; Theoretical Computer Science; Computer Science Applications1707 Computer Vision and Pattern Recognitionintegral input-to-state stabilityMathematics
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Integral Input-to-State Stability for Interconnected Discrete-Time Systems

2014

Abstract In this paper, we investigate integral input-to-state stability for interconnected discrete-time systems. The system under consideration contains two subsystems which are connected in a feedback structure. We construct a Lyapunov function for the whole system through the nonlinearly-weighted sum of Lyapunov functions of individual subsystems. We consider two cases in which we assume that one of subsystems is integral input-to-state stable and the other is either input-to-state stable or only integral input-to-state stable.

Lyapunov functionsymbols.namesakeDiscrete time and continuous timeControl and Systems EngineeringControl theoryStructure (category theory)symbolsState (functional analysis)Stability (probability)Whole systemsMathematicsIFAC Proceedings Volumes
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An LMI Approach to Exponential Stock Level Estimation for Large-Scale Logistics Networks

2013

This article aims to present a convex optimization approach for exponential stock level estimation problem of large-scale logistics networks. The model under consideration presents the dependency and interconnections between the dynamics of each single location. Using a Lyapunov function, new sufficient conditions for exponential estimation of the networks are driven in terms of linear matrix inequalities (LMIs). The explicit expression of the observer gain is parameterized based on the solvability conditions. A numerical example is included to illustrate the applicability of the proposed design method.

Lyapunov functionsymbols.namesakeMathematical optimizationActuarial scienceDependency (UML)Scale (ratio)Observer (quantum physics)Convex optimizationsymbolsParameterized complexityBusinessExpression (mathematics)Exponential function
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Stability analysis and controller design for a class of T-S fuzzy Markov jump system with uncertain expectation of packet dropouts

2013

This paper is concerned with an H∞ control for a class of Takagi-Sugeno (T-S) fuzzy Markov jump system under unreliable communication links. It is assumed that the transition probabilities determining the dynamical behavior of the underlying system are partially unknown and the communication links between the plant and the controller are imperfect (the packet dropouts occur intermittently). In this paper, a more practical scenario is considered in the setting, i.e., the expectation of packet losses represented as a description of Bernoulli-distributed stochastic process is uncertain. Attention is focused on the design of H∞ controllers such that the closed-loop system is stochastically stab…

Lyapunov functionsymbols.namesakeMathematical optimizationControl theoryStochastic processNetwork packetsymbolsStability (learning theory)Markov processFuzzy control systemFuzzy logicMathematics2013 American Control Conference
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An algorithm for solving generalized algebraic Lyapunov equations in Hilbert space, applications to boundary value problems

1988

Let L(H) be the algebra of all bounded linear operators on a separable complex Hubert space H. In a recent paper [7], explicit expressions for solutions of a boundary value problem in the Hubert space H, of the typeare given in terms of solutions of an algebraic operator equation

Lyapunov functionsymbols.namesakePure mathematicsGeneral MathematicsMathematical analysissymbolsHilbert spaceBoundary value problemAlgebraic numberMathematicsProceedings of the Edinburgh Mathematical Society
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Trajectory Decentralized Fuzzy Control of Multiple UAVs.

2008

This paper considers a complete position and heading rate control system for multiple unmanned aerial vehicles (UAVs) with constant altitude. A decentralized trajectory planning algorithm is proposed, where the UAVs will avoid collisions while moving. In order to stabilize the UAVs in the reference planned trajectories and ensure the boundedness of the control velocities, a fuzzy control law is proposed with Lyapunov's stability proof. Simulation experiments developed in Matlab environment confirm the effectiveness and the robustness of the proposed control algorithm with respect to possible turbulence disturbances perturbing the nominal motion of the UAVs.

Lyapunov stabilityLyapunov functionAutomatic controlComputer scienceTrajectory Decentralized Fuzzy Control Multiple UAVFuzzy control systemMotion controlComputer Science::Multiagent SystemsComputer Science::Roboticssymbols.namesakeSettore ING-INF/04 - AutomaticaComputer Science::Systems and ControlControl theoryControl systemTrajectorysymbolsMotion planning
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Chaos synchronization for a class of chaotic systems via H<inf>∞</inf> control technique

2013

In this paper, the robust synchronization control for a class of chaotic systems is studied. Based on linear matrix inequality techniques and Lyapunov stability theory, a novel H∝ robust synchronization controller is designed for the possible application in real engineering. Finally, some numerical simulations are included to demonstrate the effectiveness of the proposed techniques.

Lyapunov stabilityLyapunov functionsymbols.namesakeComputer simulationRobustness (computer science)Control theorySynchronization of chaosLinear matrix inequalitysymbolsRobust controlSynchronizationMathematics2013 9th Asian Control Conference (ASCC)
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Stabilization of discrete-time systems with stochastic sampling

2012

This paper is concerned with the stabilization problem of discrete-time systems with stochastic sampling. It is assumed that there are a single-rate sampling in the plant input and two stochastic sampling rates in the controller input whose occurrence probabilities are given constants and satisfy a Bernoulli distribution. By Lyapunov function approach, a new sufficient condition is presented for the mean square asymptotic stability of the system. Based on this, the design procedure for stabilization controllers is proposed. Finally, an example is given to demonstrate the effectiveness of the proposed techniques.

Mean squareLyapunov functionsymbols.namesakeExponential stabilityDiscrete time and continuous timeRobustness (computer science)Bernoulli distributionStochastic processControl theorysymbolsSampling (statistics)Mathematics2012 7th IEEE Conference on Industrial Electronics and Applications (ICIEA)
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