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Exponential Stability (exponential + stability)

Distribution by Scientific Domains
Engineering64%

Kinds of Exponential Stability

  • robust exponential stability
    		•

    Selected Abstracts

    Robust exponential stability for discrete-time interval BAM neural networks with delays and Markovian jump parameters

    INTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 9 2010
    Jiqing 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]

    Adaptive TS-FNN control for a class of uncertain multi-time-delay systems: The exponentially stable sliding mode-based approach

    INTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 4 2009
    Tung-Sheng Chiang
    Abstract This paper presents an adaptive Takagi,Sugeno fuzzy neural network (TS-FNN) control for a class of multiple time-delay uncertain nonlinear systems. First, we develop a sliding surface guaranteed to achieve exponential stability while considering mismatched uncertainty and unknown delays. This exponential stability result based on a novel Lyapunov,Krasovskii method is an improvement when compared with traditional schemes where only asymptotic stability is achieved. The stability analysis is transformed into a linear matrix inequalities problem independent of time delays. Then, a sliding mode control-based TS-FNN control scheme is proposed to achieve asymptotic stability for the controlled system. Since the TS-FNN combines TS fuzzy rules and a neural network structure, fewer numbers of fuzzy rules and tuning parameters are used compared with the traditional pure TS fuzzy approach. Moreover, all the fuzzy membership functions are tuned on-line even in the presence of input uncertainty. Finally, simulation results show the control performance of the proposed scheme. Copyright © 2008 John Wiley & Sons, Ltd. [source]

    A smooth switching adaptive controller for linearizable systems with improved transient performance

    INTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 9 2006
    Jeng Tze Huang
    Abstract The certainty equivalent control has achieved asymptotic tracking stability of linearizable systems in the presence of parametric uncertainty. However, two major drawbacks remain to be tackled, namely, the risk of running into singularity for the calculated control input and the poor transient behaviour arising frequently in a general adaptive system. For the first problem, a high gain control is activated in place of the certainty equivalent control until the risk is bypassed. Among others, it requires less control effort by taking advantages of the bounds for the input vector field. Moreover, the switching mechanism is smooth and hence avoids possible chattering behaviour. Next, to solve the second problem, a new type of update algorithm guaranteeing the exponential stability of the overall closed-loop system, on a weaker persistent excitation (PE) condition, is proposed. In particular, it requires no filtering of the regressor and hence is easier to implement. Simulation results demonstrating the validity of the proposed design are given in the final. Copyright © 2006 John Wiley & Sons, Ltd. [source]

    Improved exponential stability for stochastic Markovian jump systems with nonlinearity and time-varying delay

    INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 1 2010
    Yong He
    Abstract This paper is concerned with delay-dependent exponential stability for stochastic Markovian jump systems with nonlinearity and time-varying delay. An improved exponential stability criterion for stochastic Markovian jump systems with nonlinearity and time-varying delay is proposed without ignoring any terms by considering the relationship among the time-varying delay, its upper bound and their difference, and using both Itô's differential formula and Lyapunov stability theory. A numerical example is given to illustrate the effectiveness and the benefits of the proposed method. Copyright © 2009 John Wiley & Sons, Ltd. [source]

    Output feedback control design for station keeping of AUVs under shallow water wave disturbances

    INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 13 2009
    Shuyong Liu
    Abstract In this paper, we consider the problem of autonomous underwater vehicle (AUV) station keeping (SK) in shallow water area. During SK, an AUV is required to maintain position and orientation with respect to a fixed reference point at the sea floor. When AUV operates in shallow water, high-frequency disturbances due to waves will significantly affect the motion of the AUV. In order to derive wave disturbance information for control purposes, a nonlinear observer is first designed to estimate the shallow water wave velocities and AUV relative velocities by using position and attitude measurement. Using the observer estimates, a nonlinear output feedback controller is subsequently synthesized by applying observer backstepping technique. Global exponential stability (GES) of the proposed nonlinear observer,controller design is proved through Lyapunov stability theory. Simulation studies on a model based on an actual AUV were performed to verify the performance of the proposed nonlinear observer and output feedback controller. Copyright © 2008 John Wiley & Sons, Ltd. [source]

    Robust H, control of uncertain linear impulsive stochastic systems

    INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 13 2008
    Wu-Hua Chen
    Abstract This paper develops robust stability theorems and robust H, control theory for uncertain impulsive stochastic systems. The parametric uncertainties are assumed to be time varying and norm bounded. Impulsive stochastic systems can be divided into three cases, namely, the systems with stable/stabilizable continuous-time stochastic dynamics and unstable/unstabilizable discrete-time dynamics, the systems with unstable/unstabilizable continuous dynamics and stable/stabilizable discrete-time dynamics, and the systems in which both the continuous-time stochastic dynamics and the discrete-time dynamics are stable/stabilizable. Sufficient conditions for robust exponential stability and robust stabilization for uncertain impulsive stochastic systems are derived in terms of an average dwell-time condition. Then, a linear matrix inequality-based approach to the design of a robust H, controller for each system is presented. Finally, the numerical examples are provided to demonstrate the effectiveness of the proposed approach. Copyright © 2007 John Wiley & Sons, Ltd. [source]

    Exponential estimates for neutral time delay systems with multiple delays

    INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 2 2006
    Vladimir Kharitonov
    Abstract Exponential estimates and sufficient conditions for the exponential stability of linear neutral time delay for systems with multiple delays are given. The case of systems with uncertainties, including uncertainties in the difference operator, is considered. The proofs follows from new results on non-homogeneous difference equations evolving in continuous time combined with the Lyapunov,Krasovskii functionals approach. The conditions are expressed in terms of linear matrix inequalities. The particular case of neutral time delay systems with commensurate delays, which leads to less restrictive exponential estimates, is also addressed. Copyright © 2005 John Wiley & Sons, Ltd. [source]

    Nonlinear controls for a class of discrete-time bilinear systems

    INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 11 2003
    Min-Shin Chen
    Abstract For a discrete-time neutrally stable bilinear system, a nonlinear state feedback control based on the passivity design has been proposed to stabilize the system globally and asymptotically. This paper shows that the decay rate resulting from the passivity control is not exponential, and the system's response speed becomes very sluggish asymptotically. A ,normalized' nonlinear control is therefore proposed to achieve exponential stability. The new exponentially stabilizing control not only improves the system's response speed, but also enhances the system's robustness against small parametric perturbations. Copyright © 2003 John Wiley & Sons, Ltd. [source]

    Adaptive exponential stabilization of mobile robots with unknown constant-input disturbance

    JOURNAL OF FIELD ROBOTICS (FORMERLY JOURNAL OF ROBOTIC SYSTEMS), Issue 6 2001
    Weiguo Wu
    This paper concentrates on the discussions on stabilization of mobile robots with unknown constant-input disturbance. Continuous time-varying adaptive controllers are designed for mobile robots in a chain-form by using Lyapunov approach. With the property of homogeneous systems, uncertain mobile robots governed by the proposed control algorithms become homogeneous of order 0 to achieve exponential stability. Simulation results validate the theoretical analysis. © 2001 John Wiley & Sons, Inc. [source]

    Polynomial and analytic stabilization of a wave equation coupled with an Euler,Bernoulli beam

    MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 5 2009
    Kaïs Ammari
    Abstract We consider a stabilization problem for a model arising in the control of noise. We prove that in the case where the control zone does not satisfy the geometric control condition, B.L.R. (see Bardos et al. SIAM J. Control Optim. 1992; 30:1024,1065), we have a polynomial stability result for all regular initial data. Moreover, we give a precise estimate on the analyticity of reachable functions where we have an exponential stability. Copyright © 2008 John Wiley & Sons, Ltd. [source]

    Multidimensional Hele-Shaw flows modelling Stokesian fluids

    MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 5 2009
    Joachim Escher
    Abstract We consider here an n -dimensional periodic flow describing the motion of an incompressible Stokesian fluid in a Hele-Shaw cell. The free surface separating the fluid from air, at pressure normalized to be zero, is moving under the influence of gravity and surface tension. We prove the existence of a unique classical Hölder solution for small perturbations of cylinders. Moreover, we evidence the existence of a single steady state and prove its exponential stability. Copyright © 2008 John Wiley & Sons, Ltd. [source]

    Riesz basis and stabilization for the flexible structure of a symmetric tree-shaped beam network

    MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 3 2008
    Jun-Min Wang
    Abstract The stabilization of a symmetric tree-shaped network of Euler,Bernoulli beams described by a system of partial differential equations is considered. The boundary controllers are designed based on passivity principle. The eigenfrequencies are analysed in detail and the asymptotic expansion of eigenvalues are presented. It is shown that there is a set of generalized eigenfunctions for the closed-loop system, which forms a Riesz basis with parentheses for the energy state space. This concludes the spectrum-determined growth condition and the exponential stability of the closed-loop system. Copyright © 2007 John Wiley & Sons, Ltd. [source]

    Existence and exponential stability in Lr -spaces of stationary Navier,Stokes flows with prescribed flux in infinite cylindrical domains

    MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 2 2007
    Myong-Hwan Ri
    Abstract We prove existence, uniqueness and exponential stability of stationary Navier,Stokes flows with prescribed flux in an unbounded cylinder of ,n,n,3, with several exits to infinity provided the total flux and external force are sufficiently small. The proofs are based on analytic semigroup theory, perturbation theory and Lr , Lq -estimates of a perturbation of the Stokes operator in Lq -spaces. Copyright © 2006 John Wiley & Sons, Ltd. [source]

    Low-gain adaptive stabilization of semilinear second-order hyperbolic systems

    MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 18 2004
    Toshihiro Kobayashi
    Abstract In this paper low-gain adaptive stabilization of undamped semilinear second-order hyperbolic systems is considered in the case where the input and output operators are collocated. The linearized systems have an infinite number of poles and zeros on the imaginary axis. The adaptive stabilizer is constructed by a low-gain adaptive velocity feedback. The closed-loop system is governed by a non-linear evolution equation. First, the well-posedness of the closed-loop system is shown. Next, an energy-like function and a multiplier function are introduced and the exponential stability of the closed-loop system is analysed. Some examples are given to illustrate the theory. Copyright © 2004 John Wiley & Sons, Ltd. [source]

    Thermoelasticity with second sound,exponential stability in linear and non-linear 1-d

    MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 5 2002
    Reinhard Racke
    We consider linear and non-linear thermoelastic systems in one space dimension where thermal disturbances are modelled propagating as wave-like pulses travelling at finite speed. This removal of the physical paradox of infinite propagation speed in the classical theory of thermoelasticity within Fourier's law is achieved using Cattaneo's law for heat conduction. For different boundary conditions, in particular for those arising in pulsed laser heating of solids, the exponential stability of the now purely, but slightly damped, hyperbolic linear system is proved. A comparison with classical hyperbolic,parabolic thermoelasticity is given. For Dirichlet type boundary conditions,rigidly clamped, constant temperature,the global existence of small, smooth solutions and the exponential stability are proved for a non-linear system. Copyright © 2002 John Wiley & Sons, Ltd. [source]

    Non-linear stability in the Bénard problem for a double-diffusive mixture in a porous medium

    MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 16 2001
    S. Lombardo
    The linear and non-linear stability of a horizontal layer of a binary fluid mixture in a porous medium heated and salted from below is studied, in the Oberbeck,Boussinesq,Darcy scheme, through the Lyapunov direct method. This is an interesting geophysical case because the salt gradient is stabilizing while heating from below provides a destabilizing effect. The competing effects make an instability analysis difficult. Unconditional non-linear exponential stability is found in the case where the normalized porosity , is equal to one. For other values of , a conditional stability theorem is proved. In both cases we demonstrate the optimum result that the linear and non-linear critical stability parameters are the same whenever the Principle of Exchange of Stabilities holds. Copyright © 2001 John Wiley & Sons, Ltd. [source]

    Delay-dependent exponential stability for switched delay systems

    OPTIMAL CONTROL APPLICATIONS AND METHODS, Issue 4 2009
    Dong Wang
    Abstract Delay-dependent exponential stability criteria are presented for switched systems consisting of a family of stable and unstable subsystems with interval time-varying delay. Two cases with regard to such delay are considered: one is that time-varying delay function is differentiable and bounded and the other is that time-varying delay function is continuous and bounded. It is very difficult to analyze the stability of such systems due to the existence of time delay and unstable subsystems. By introducing some free-weighting matrices, constructing the new Lyapunov,Krasovskii functional and taking advantage of the average dwell time technique, not only is this difficulty overcome but also sufficient conditions for such criteria are obtained and formulated in terms of linear matrix inequalities. Numerical examples are provided to demonstrate the effectiveness and feasibility of the proposed approaches. Copyright © 2008 John Wiley & Sons, Ltd. [source]

    Mean square exponential stability of generalized stochastic neural networks with time-varying delays,

    ASIAN JOURNAL OF CONTROL, Issue 6 2009
    Jianjiang Yu
    Abstract In this paper, the mean square exponential stability problem is dealt with a class of uncertain generalized stochastic neural networks with time-varying delays. By introducing a new Lyapunov-Krasovskii functional, improved delay-dependent stability criteria are established in terms of linear matrix inequalities. The activation functions are assumed to be of more general descriptions, which generalize and improve those earlier methods. Finally, a numerical example is given to show that our results are less conservative and more efficient than the existing stability criteria. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society [source]

    Improved exponential estimates for neutral systems

    ASIAN JOURNAL OF CONTROL, Issue 3 2009
    Zhan Shu
    Abstract Improved exponential estimates and a new sufficient condition for the exponential stability of neutral type time-delay systems are established in terms of linear matrix inequalities (LMIs). A new Lyapunov-Krasovskii functional candidate with appropriately constructed exponential terms is introduced to prove the exponential stability and to reduce the conservatism. For the uncertain case, a corresponding condition for the robust exponential stability is also given. It is shown by numerical examples that the proposed conditions are less conservative than existing results. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society [source]

    A new adaptive backstepping Coulomb friction compensator for servo control systems,

    ASIAN JOURNAL OF CONTROL, Issue 1 2009
    Jen-te Yu
    Abstract A new Coulomb friction compensator is proposed for servo control systems in this paper. The novelty of the new approach lies in its capability of assigning the eigenvalues of the resulting closed loop system while attacking the problem. First, based on the standard backstepping methodology, an implicit Lyapunov function, with part of the components being only symbolically constructed at the very beginning, is utilized. To increase the robustness of the system against disturbance and model inaccuracy, an integral term is employed in the design. Using part of the variable gradient method, we are able to turn the implicit Lyapunov function into an explicit one, which is positive definite, and whose time-derivative is negative definite. Second, it will be shown that the resulting closed loop error system is a switched linear system with two possible active modes that share the same set of eigenvalues, which is at our disposal. Unlike the common adaptive control design methods, such as the Control Lyapunov Function approach, in which the gains are typically positive but otherwise arbitrary, and are hence difficult to choose and have a lack of connection with the system's performance, our new scheme imposes two further constraints on the gains. It turns out that we can then match these gains with the coefficients of the desired characteristic equation of the closed loop system. In this respect, the gains are linked to the system's overall performance, which is a new and very appealing feature for such a scheme. Finally, a procedure of constructing a common Lyapunov function is provided to prove exponential stability of the aforementioned switched linear system. In addition, using the invariance principle, we will show the convergence of the estimated Coulomb friction coefficient to its real value. Numerical simulations are given to validate the effectiveness of the design and its robustness against friction time-variations. Compared to existing results, the proposed scheme is much simpler, hence, much more advantageous computationally. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society [source]

    Network-based robust H, control of continuous-time systems with uncertainty,

    ASIAN JOURNAL OF CONTROL, Issue 1 2009
    Xun-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]

    GENERALIZED QUADRATIC STABILIZATION FOR DISCRETE-TIME SINGULAR SYSTEMS WITH TIME-DELAY AND NONLINEAR PERTURBATION

    ASIAN JOURNAL OF CONTROL, Issue 3 2005
    Guoping Lu
    ABSTRACT This paper discusses a generalized quadratic stabilization problem for a class of discrete-time singular systems with time-delay and nonlinear perturbation (DSSDP), which the satisfies Lipschitz condition. By means of the S-procedure approach, necessary and sufficient conditions are presented via a matrix inequality such that the control system is generalized quadratically stabilizable. An explicit expression of the static state feedback controllers is obtained via some free choices of parameters. It is shown in this paper that generalized quadratic stability also implies exponential stability for linear discrete-time singular systems or more generally, DSSDP. In addition, this new approach for discrete singular systems (DSS) is developed in order to cast the problem as a convex optimization involving linear matrix inequalities (LMIs), such that the controller can stabilize the overall system. This approach provides generalized quadratic stabilization for uncertain DSS and also extends the existing robust stabilization results for non-singular discrete systems with perturbation. The approach is illustrated here by means of numerical examples. [source]

    Chemical networks with inflows and outflows: A positive linear differential inclusions approach

    BIOTECHNOLOGY PROGRESS, Issue 3 2009
    David Angeli
    Abstract Certain mass-action kinetics models of biochemical reaction networks, although described by nonlinear differential equations, may be partially viewed as state-dependent linear time-varying systems, which in turn may be modeled by convex compact valued positive linear differential inclusions. A result is provided on asymptotic stability of such inclusions, and applied to a ubiquitous biochemical reaction network with inflows and outflows, known as the futile cycle. We also provide a characterization of exponential stability of general homogeneous switched systems which is not only of interest in itself, but also plays a role in the analysis of the futile cycle. © 2009 American Institute of Chemical Engineers Biotechnol. Prog., 2009 [source]