Lyapunov's stability theory

This study presents web handling systems with the characteristic of a changing moment of inertia and operating radius of rolls. Commonly, sliding mode control (SMC) is used to control the web tension of this system due to its robustness against modeling imprecision.

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In this paper, a sliding mode controller is proposed for global synchronization between two chaotic systems. The interesting point of this controller is that it can help reduce the synchronization time based on the selection of the appropriate gain parameter.

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(BQ) Ebook Dynamical systems with applications using Matlab (Second Edition): Part 1 includes the following content: Limit cycles; hamiltonian systems, lyapunov functions, and stability; bifurcation theory; three-dimensional autonomous systems and chaos; poincaré maps and nonautonomous systems in the plane; local and global bifurcations; the second part of hilbert’s sixteenth problem; neural networks; chaos control and synchronization; binary oscillator computing; simulink; examination-type questions; solutions to exercises.

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This control structure is inflexible since using fixed gains. For overcoming this weakness, we integrate variable fractional-order derivative into SMC that leads to an adaptive system with adjustable parameters. We use Mittag–Leffler stability, an enhanced version of Lyapunov theory, to analyze the convergence of closed-loop system. Applying the controller to a practical crane shows the efficiency of proposed control approach. The controller works well and keeps the output responses consistent despite the large variation of crane parameters.

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Fractional calculus (FC) is widely used in many interdisciplinary branches of science due to its effectiveness in describing and investigating complicated phenomena. In this work, nonlinear dynamics for a new physical model using nonlocal fractional differential operator with singular kernel is introduced. New Routh-Hurwitz stability conditions are derived for the fractional case as the order lies in [0,2). The new and basic Routh-Hurwitz conditions are applied to the commensurate case. The local stability of the incommensurate orders is also discussed.

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The stability problem for a class of stochastic neural networks with Markovian jump parameters and leakage delay is addressed in this study. The sufficient condition to ensure an exponentially stable stochastic neural networks system is presented and proven with Lyapunov functional theory, stochastic stability technique and linear matrix inequality method.

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This is the main result of the paper. We use the method to estimate the region of attraction for the case of the asymptotical stability. We study this technique for the case autonomous systems.

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In this paper, a nonlinear optimal control law based on aggregated variables is presented. The criterion is chosen so that the dynamic characteristics of object are included. The stability of the closed-loop system is global according to the Lyapunov stability theory. The control law depends explicitly on ship model parameters, so that it is can be easily to tune when the parameters change.

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s. The first one is to establish and optimize parameters of a sliding mode controller (SMC). The next is to design a fuzzy logic system to expand the ability of the SMC to face with the larger ranges of the load variation. The DUO is used to compensate for disturbance and uncertainty. By using the ANFIS-I-MRD and the control force estimated by the FDIC, current for the MRD at each time for stamping out chassis vibration is specified. The stability of the FDIC is analyzed via Lyapunov stability theory.

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T he impetus to produce this book came in a brief phone call in 1998. Chuck Crumly, of Academic Press, called with an invitation and a deadline. Either The Ecology of Fishes on Coral Reefs, published in 1991, would be allowed to lapse into out-of-print status, or I would agree to produce a second edition. Looking back on all the work, I suspect it might have been wiser to say, "Let her lapse." But I didn't.

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Modern complex dynamical systems1 are highly interconnected and mutually interdependent, both physically and through a multitude of information and communication network constraints. The sheer size (i.e., dimensionality) and complexity of these large-scale dynamical systems often necessitates a hierarchical decentralized architecture for analyzing and controlling these systems. Specifically, in the analysis and control-system design of complex large-scale dynamical systems it is often desirable to treat the overall system as a collection of interconnected subsystems.

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EXISTENCE AND GLOBAL STABILITY OF POSITIVE PERIODIC SOLUTIONS OF A DISCRETE PREDATOR-PREY SYSTEM WITH DELAYS LIN-LIN WANG, WAN-TONG LI, AND PEI-HAO ZHAO Received 13 January 2004 We study the existence and global stability of positive periodic solutions of a periodic discrete predator-prey system with delay and Holling type III functional response. By using the continuation theorem of coincidence degree theory and the method of Lyapunov functional, some sufficient conditions are obtained. 1.

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Stability Issues in RNN Architectures Perspective The focus of this chapter is on stability and convergence of relaxation realised through NARMA recurrent neural networks. Unlike other commonly used approaches, which mostly exploit Lyapunov stability theory, the main mathematical tool employed in this analysis is the contraction mapping theorem (CMT), together with the fixed point iteration (FPI) technique. This enables derivation of the asymptotic stability (AS) and global asymptotic stability (GAS) criteria for neural relaxive systems.

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