Search results for "Exponential stability"
showing 10 items of 84 documents
Numerical study of soliton stability, resolution and interactions in the 3D Zakharov–Kuznetsov equation
2021
International audience; We present a detailed numerical study of solutions to the Zakharov-Kuznetsov equation in three spatial dimensions. The equation is a three-dimensional generalization of the Korteweg-de Vries equation, though, not completely integrable. This equation is L-2-subcritical, and thus, solutions exist globally, for example, in the H-1 energy space.We first study stability of solitons with various perturbations in sizes and symmetry, and show asymptotic stability and formation of radiation, confirming the asymptotic stability result in Farah et al. (0000) for a larger class of initial data. We then investigate the solution behavior for different localizations and rates of de…
Diffusive neural network
2002
Abstract A non-connectionist model of a neuronal network based on passive diffusion of neurotransmitters is presented as an alternative to hard-wired artificial neural networks. Classic thermodynamical approach shows that the diffusive network is capable of exhibiting asymptotic stability and a dynamics resembling that of a chaotic system. Basic computational capabilities of the net are discussed based on the equivalence with a Turing machine. The model offers a way to represent mass-sustained brain functions in terms of recurrent behaviors in the phase space.
Asynchronously switched control of discrete impulsive switched systems with time delays
2013
This paper is concerned with the stabilization problem for a class of uncertain discrete impulsive switched delay systems under asynchronous switching. The so-called asynchronous switching means that the switches between the candidate controllers and system modes are asynchronous. By using the average dwell time (ADT) approach, sufficient conditions for the existence of an asynchronously switched controller is derived such that the resulting closed-loop system is exponentially stable. The desired controller gains and the admissible switching signals are obtained in terms of a set of matrix inequalities. A numerical example is given to illustrate the effectiveness of the proposed method.
Exponential stability analysis of Markovian jump nonlinear systems with mixed time delays and partially known transition probabilities
2013
In this paper, the problem of exponential stability is studied for a class of Markovian jump neutral nonlinear systems with mixed neutral and discrete time delays. By Lyapunov-Krasovskii function approach, a novel mean-square exponential stability criterion is derived for the situation that the system's transition rates are partially or completely accessible. Finally, some numerical examples are provided to illustrate the effectiveness of the proposed methods.
Robust synchronization and fault detection of uncertain master-slave systems with mixed time-varying delays and nonlinear perturbations
2011
Publiahed version of an article in the journal: International Journal of Control, Automation and Systems. Also available from the publisher on SpringerLink: http://dx.doi.org/10.1007/s12555-011-0408-8 In this paper, the problem of robust synchronization and fault detection for a class of master-slave systems subjected to some nonlinear perturbations and mixed neutral and discrete time-varying delays is investigated based on an H ∞ performance condition. By introducing a descriptor technique, using Lyapunov-Krasovskii functional and a suitable change of variables, new required sufficient conditions are established in terms of delay-dependent linear matrix inequalities to synthesize the resid…
Observer-Based Stabilization of Stochastic Systems with Limited Communication
2012
Published version of an article in the journal: Mathematical Problems in Engineering. Also available from Hindawi: http://dx.doi.org/10.1155/2012/781542 Open Access This paper studies the problem of observer-based stabilization of stochastic nonlinear systems with limited communication. A communication channel exists between the output of the plant and the input of the dynamic controller, which is considered network-induced delays, data packet dropouts, and measurement quantization. A new stability criterion is derived for the stochastic nonlinear system by using the Lyapunov functional approach. Based on this, the design procedure of observer-based controller is presented,which ensures asy…
Vibration control of vehicle engine-body systems with time delay: an LMI approach
2013
The objective of this chapter is to study the problem of vibration control analysis and synthesis in a vehicle engine-body vibration structure. It is assumed that the actuator is subject to a time-varying delay for control of bounce and pitch vibrations. Based on a Lyapunov-Krasovskii functional and using some free weighting matrices, delay-dependent sufficient conditions for designing desired state- and output-feedback controllers are given in terms of linear matrix inequalities (LMIs). The state- and output-feedback controllers, which guarantee asymptotic stability with a prescribed γ-level L2-gain (or H∞ performance), are then developed directly instead of coupling the second-order model…
A convex optimization approach for vibration control of base isolated structures with limited wireless communication capacity
2010
The problem of H ∞ control design for vibration reduction of a base isolated structure with limited wireless communication capacity is studied in this paper. The network under consideration is subjected to measurement quantization, signal transmission delay, and data packet dropout, which appear typically in a network environment. Based on Lyapunov-Krasovskii functional (LKF) theory, some delay-range-dependent conditions are established for the existence of desired controllers such that the resulting closed-loop system is asymptotically stable and its performance is kept within a prescribed level. Finally, some simulation results are given to illustrate the effectiveness of our method.
Feedback vibration control of a base-isolated building with delayed measurements using h<inf>&#x221E;</inf> techniques
2010
In this paper we address the problem of vibration reduction of buildings with delayed measurements, where the delays are time-varying and bounded. We focus on a convex optimization approach to the problem of state-feedback H ∞ control design. An appropriate Lyapunov-Krasovskii functional and some free weighting matrices are used to establish some delay-range-dependent sufficient conditions for the design of desired controllers in terms of linear matrix inequalities (LMIs). The controller, which guarantees asymptotic stability and an H ∞ performance, simultaneously, for the closed-loop system of the structure, is then developed. The performance of the controller is evaluated through the simu…
Localization from inertial data and sporadic position measurements
2020
International audience; A novel estimation strategy for inertial navigation in indoor/outdoor environments is proposed with a specific attention to the sporadic nature of the non-periodic measurements. After introducing the inertial navigation model, we introduce an observer providing an asymptotic estimate of the plant state. We use a hybrid dynamical systems representation for our results, in order to provide an effective, and elegant theoretical framework. The estimation error dynamics with the proposed observer shows a peculiar cascaded interconnection of three subsystems (allowing for intuitive gain tuning), with perturbations occurring either on the jump or on the flow dynamics (depen…