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Lyapunov Functional (lyapunov + functional)
Selected AbstractsRobust exponential stability for discrete-time interval BAM neural networks with delays and Markovian jump parametersINTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 9 2010Jiqing Qiu Abstract This paper investigates the problem of global robust exponential stability for discrete-time interval BAM neural networks with mode-dependent time delays and Markovian jump parameters, by utilizing the Lyapunov,Krasovskii functional combined with the linear matrix inequality (LMI) approach. A new Markov process as discrete-time, discrete-state Markov process is considered. An exponential stability performance analysis result is first established for error systems without ignoring any terms in the derivative of Lyapunov functional by considering the relationship between the time-varying delay and its upper bound. The delay factor depends on the mode of operation. Three numerical examples are given to demonstrate the merits of the proposed method. Copyright © 2010 John Wiley & Sons, Ltd. [source] Delay-dependent stability and stabilization of neutral time-delay systemsINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 12 2009Jian Sun Abstract This paper is concerned with the problem of stability and stabilization of neutral time-delay systems. A new delay-dependent stability condition is derived in terms of linear matrix inequality by constructing a new Lyapunov functional and using some integral inequalities without introducing any free-weighting matrices. On the basis of the obtained stability condition, a stabilizing method is also proposed. Using an iterative algorithm, the state feedback controller can be obtained. Numerical examples illustrate that the proposed methods are effective and lead to less conservative results. Copyright © 2008 John Wiley & Sons, Ltd. [source] Delay-dependent robust stability for stochastic time-delay systems with polytopic uncertaintiesINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 15 2008Hongyi Li Abstract This paper considers a delay-dependent and parameter-dependent robust stability criterion for stochastic time-delay systems with polytopic uncertainties. The delay-dependent robust stability criterion, as expressed in terms of linear matrix inequalities (LMIs), is obtained by using parameter-dependent Lyapunov functions. It is shown that the result derived by a parameter-dependent Lyapunov functional is less conservative. Numerical examples are provided to illustrate the effectiveness of the proposed method. Copyright © 2008 John Wiley & Sons, Ltd. [source] Augmented Lyapunov functional and delay-dependent stability criteria for neutral systemsINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 18 2005Yong He Abstract In this paper, an augmented Lyapunov functional is proposed to investigate the asymptotic stability of neutral systems. Two methods with or without decoupling the Lyapunov matrices and system matrices are developed and shown to be equivalent to each other. The resulting delay-dependent stability criteria are less conservative than the existing ones owing to the augmented Lyapunov functional and the introduction of free-weighting matrices. The delay-independent criteria are obtained as an easy corollary. Numerical examples are given to demonstrate the effectiveness and less conservativeness of the proposed methods. Copyright © 2005 John Wiley & Sons, Ltd. [source] Uniform stabilization of a one-dimensional hybrid thermo-elastic structureMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 14 2003Marié Grobbelaar-Van Dalsen Abstract This paper is concerned with the stabilization of a one-dimensional hybrid thermo-elastic structure consisting of an extensible thermo-elastic beam which is hinged at one end with a rigid body attached to its free end. The model takes account of the effect of stretching on bending and rotational inertia. The property of uniform stability of the energy associated with the model is asserted by constructing an appropriate Lyapunov functional for an abstract second order evolution problem. Critical use is made of a multiplier of an operator theoretic nature, which involves the fractional power A,1/2 of the bi-harmonic operator pair A acting in the abstract evolution problem. An explicit decay rate of the energy is obtained. Copyright © 2003 John Wiley & Sons, Ltd. [source] Novel stability criteria for bidirectional associative memory neural networks with time delaysINTERNATIONAL JOURNAL OF CIRCUIT THEORY AND APPLICATIONS, Issue 5 2002Xiaofeng Liao Abstract In this paper, the bidirectional associative memory (BAM) neural network with axonal signal transmission delay is considered. This model is also referred to as a delayed dynamic BAM model. By combining a number of different Lyapunov functionals with the Razumikhin technique, some sufficient conditions for the existence of a unique equilibrium and global asymptotic stability of the network are derived. These results are fairly general and can be easily verified. Besides, the approach for the analysis allows one to consider several different types of activation functions, including piecewise linear sigmoids with bounded activations as well as C1 -smooth sigmoids. It is believed that these results are significant and convenient in the design and applications of BAM neural networks. Copyright © 2002 John Wiley & Sons, Ltd. [source] A delay decomposition approach to delay-dependent stability for linear systems with time-varying delaysINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 17 2009Xian-Ming Zhang Abstract This paper is concerned with delay-dependent stability for linear systems with time-varying delays. By decomposing the delay interval into multiple equidistant subintervals, on which different Lyapunov functionals are chosen, and new Lyapunov-Krasvskii functionals are then constructed. Employing these new Lyapunov-Krasvskii functionals, some new delay-dependent stability criteria are established. The numerical examples show that the obtained results are less conservative than some existing ones in the literature. Copyright © 2009 John Wiley & Sons, Ltd. [source] Network-based robust H, control of continuous-time systems with uncertainty,ASIAN JOURNAL OF CONTROL, Issue 1 2009Xun-Lin Zhu Abstract This paper studies the problem of robust H, control for continuous-time networked control systems (NCSs). A new type of Lyapunov functionals is exploited to derive sufficient conditions for guaranteeing the robust exponential stability and H, performance of the considered system. It is shown that the new result is less conservative than the existing corresponding ones. Meanwhile, a method of eliminating redundant variables to reduce computational complexity is given, which is also applied to design state feedback H, controllers, and the design condition is given in terms of solutions to a set of linear matrix inequalities (LMIs). Numerical examples are given to illustrate the effectiveness of the proposed methods. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society [source] On the convergence rate of vanishing viscosity approximationsCOMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 8 2004Alberto Bressan Given a strictly hyperbolic, genuinely nonlinear system of conservation laws, we prove the a priori bound ,u(t, ·) , u,(t, ·), = O(1)(1 + t) · |ln ,| on the distance between an exact BV solution u and a viscous approximation u,, letting the viscosity coefficient , , 0. In the proof, starting from u we construct an approximation of the viscous solution u, by taking a mollification u * and inserting viscous shock profiles at the locations of finitely many large shocks for each fixed ,. Error estimates are then obtained by introducing new Lyapunov functionals that control interactions of shock waves in the same family and also interactions of waves in different families. © 2004 Wiley Periodicals, Inc. [source] | |||||||||||||