Wyniki wyszukiwania - Biblioteka Nauki

1

The interval parabolic system

100%

Oprzedkiewicz K.

Archives of Control Sciences

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2003

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tom Vol. 13, no. 4

415-430

EN

In the paper a nem interval model for the uncertain, parabolic time invariant system is presented. System under consideration is described by model with two dimensional uncertain parameters space. In this case the simple geometric interpretation of the system spectrum and it's decopmosition can be presented. The proposed spectrum decomposition conditions are based on the geometric interpretation of the system spectrum. the results are by the examples depicted.

2

Wellposedness and exponential decay rates for the Moore-Gibson-Thompson equation arising in high intensity ultrasound

100%

Kaltenbacher B. , Lasiecka I. , Marchand R.

Control and Cybernetics

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2011

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tom Vol. 40, no 4

971-988

EN

We consider the Moore-Gibson-Thompson equation which arises, e.g., as a linearization of a model for wave propagation in viscous thermally relaxing fluids. This third order in time equation displays, even in the linear version, a variety of dynamical behaviors for their solutions that depend on the physical parameters in the equation. These range from non-existence and instability to exponential stability (in time). It will be shown that by neglecting diffusivity of the sound coefficient there arises a lack of existence of a semigroup associated with the linear dynamics. More specifically, the corresponding linear dynamics consists of three diffusions: two backward and one forward. When diffusivity of the sound is positive, the linear dynamics is described by a strongly continuous semigroup which is exponentially stable when the ratio of sound speed×relaxation parameter/ sound diffusivity is sufficiently small, and unstable in the complementary regime. The theoretical estimates proved in the paper are confirmed by numerical validation.

3

Qualitative aspects of solutions in resonators

100%

Quintanilla R. , Racke R.

Archives of Mechanics

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2008

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tom Vol. 60, nr 4

345-360

EN

We consider the system of micro-beam resonators in the thermoelastic theory of Lord and Shulmann. First, we prove the uniqueness and instability of solutions when the sign of a parameter is not prescribed. Existence of solutions and uniform bounds for the real part of the spectrum have been found. We finish the paper by proving the impossibility of the time localization of solutions.

4

Less conservative results for the exponential stability of uncertain time-delay systems

100%

Sun Y. J.

Control and Cybernetics

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2005

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tom Vol. 34, no 4

1045-1055

EN

In this paper, global exponential stability of a class of uncertain systems with multiple time delays is investigated. Simple delay-independent criterion is derived to guarantee the global exponential stability of such systems. The main result is sharper than the recent result reported in the literature. Two numerical examples are also provided to illustrate the main result.

5

Polynomial stability of evolution operators in Banach spaces

100%

Megan M. , Ceausu T. , Ramneantu M. L.

Opuscula Mathematica

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2011

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tom Vol. 31, no. 2

279-288

EN

The paper considers three concepts of polynomial stability for linear evolution operators which are defined in a general Banach space and whose norms can increase not faster than exponentially. Our approach is based on the extension of techniques for exponential stability to the case of polynomial stability. Some illustrating examples clarify the relations between the stability concepts considered in paper. The obtained results are generalizations of well-known theorems about the uniform and nonuniform exponential stability.

6

Exponential stability of nonlinear non-autonomous multivariable systems

100%

Gil' M.

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tom 35

|

nr 1

89-100

EN

We consider nonlinear non-autonomous multivariable systems governed by differential equations with differentiable linear parts. Explicit conditions for the exponential stability are established. These conditions are formulated in terms of the norms of the derivatives and eigenvalues of the variable matrices, and certain scalar functions characterizing the nonlinearity. Moreover, an estimate for the solutions is derived. It gives us a bound for the region of attraction of the steady state. As a particular case we obtain absolute stability conditions. Our approach is based on a combined usage of the properties of the "frozen" Lyapunov equation, and recent norm estimates for matrix functions. An illustrative example is given.

7

Limits of stabilization of a networked hyperbolic system with a circle

100%

Gugat M. , Huang X. , Wang Z.

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tom Vol. 52, No. 1

79--121

EN

This paper is devoted to the discussion of the exponential stability of a networked hyperbolic system with a circle. Our analysis extends an example by Bastin and Coron about the limits of boundary stabilizability of hyperbolic systems to the case of a networked system that is defined on a graph which contains a cycle. By spectral analysis, we prove that the system is stabilizable while the length of the arcs is sufficiently small. However, if the length of the arcs is too large, the system is not stabilizable. Our results are robust with respect to small perturbations of the arc lengths. Complementing our analysis, we provide numerical simulations that illustrate our findings.

8

Exponential stability and blow up for a problem with Balakrishnan-Taylor damping

88%

Tatar N.-E. , Zaraï A.

|

2011

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tom Vol. 44, nr 1

67-90

EN

This work is devoted to the study of a nonlinear viscoelastic Kirchhoff equation with Balakrishnan-Taylor damping. We show that the weak dissipation producedby the memory term is strong enough to stabilize solutions exponentially. Also, we show that a nonlinear source of polynomial type is able to force solutions to blow up in finite time even in presence of a stronger damping.

9

A variable structure observer for the control of robot manipulators

88%

Abdessameud A. , Khelfi M. F.

International Journal of Applied Mathematics and Computer Science

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2006

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tom 16

|

nr 2

189-196

EN

This paper deals with the application of a variable structure observer developed for a class of nonlinear systems to solve the trajectory tracking problem for rigid robot manipulators. The analyzed approach to observer design proposes a simple design methodology for systems having completely observable linear parts and bounded nonlinearities andor uncertainties. This observer is basically the conventional Luenberger observer with an additional switching term that is used to guarantee robustness against modeling errors and system uncertainties. To solve the tracking problem, we use a control law developed for robot manipulators in the full information case. The closed loop system is shown to be globally asymptotically stable based on Lyapunov arguments. Simulation results on a 3-DOF robot manipulator show the asymptotic convergence of the vectors of observation and tracking errors.

10

Observer-based controller design of time-delay systems with an interval time-varying delay

88%

Thuan M. , Phat V. , Trinh H.

|

nr 4

921-927

EN

This paper considers the problem of designing an observer-based output feedback controller to exponentially stabilize a class of linear systems with an interval time-varying delay in the state vector. The delay is assumed to vary within an interval with known lower and upper bounds. The time-varying delay is not required to be differentiable, nor should its lower bound be zero. By constructing a set of Lyapunov-Krasovskii functionals and utilizing the Newton-Leibniz formula, a delay-dependent stabilizability condition which is expressed in terms of Linear Matrix Inequalities (LMIs) is derived to ensure the closed-loop system is exponentially stable with a prescribed α-convergence rate. The design of an observerbased output feedback controller can be carried out in a systematic and computationally efficient manner via the use of an LMI-based algorithm. A numerical example is given to illustrate the design procedure.

11

Extended lie algebraic stability analysis for switched systems with continuous-time and discrete-time subsystems

88%

Zhai G. , Xu X. , Lin H. , Liu D.

International Journal of Applied Mathematics and Computer Science

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2007

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tom 17

|

nr 4

447-454

EN

We analyze stability for switched systems which are composed of both continuous-time and discrete-time subsystems. By considering a Lie algebra generated by all subsystem matrices, we show that if all subsystems are Hurwitz/Schur stable and this Lie algebra is solvable, then there is a common quadratic Lyapunov function for all subsystems and thus the switched system is exponentially stable under arbitrary switching. When not all subsystems are stable and the same Lie algebra is solvable, we show that there is a common quadratic Lyapunov-like function for all subsystems and the switched system is exponentially stable under a dwell time scheme. Two numerical examples are provided to demonstrate the result.

12

Local attractivity in nonautonomous semilinear evolution equations

88%

Blot J. , Buşe C. , Cieutat P.

Nonautonomous Dynamical Systems

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2014

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tom 1

|

nr 1

EN

We study the local attractivity of mild solutions of equations in the form u’(t) = A(t)u(t) + f (t, u(t)), where A(t) are (possible) unbounded linear operators in a Banach space and where f is a (possible) nonlinear mapping. Under conditions of exponential stability of the linear part, we establish the local attractivity of various kinds of mild solutions. To obtain these results we provide several results on the Nemytskii operators on the space of the functions which converge to zero at infinity

13

Exponential stability of interval dynamical systems with quadratic nonlinearity

88%

Ivlev R. , Sokolova S.

Systems Science

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2006

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tom Vol. 32, no 1

5-14

EN

This article proposes an approach for investigating the exponential stability of a nonlinear interval dynamical system with the nonlincarily of a quadratic type on the basis of Lyapunov's direct method. It also constructs an inner estimate of the attraction domain to the origin for the system under consideration.

14

An outline of the linear control system synthesis by a proper, stable rational functions approach

75%

Ładziński R.

Archives of Control Sciences

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1998

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tom Vol. 7, no. 3/4

241-265

EN

In the process of designing controllers for linear multivariable plants specially effective are algebraic methods which require from the transfer matrices of both, the plant and the controller to be presented in coprime fractional form with factorization carried on with respect to the ring of exponentially-stable, proper real-rational functions. The main objective of the paper is to show that this form of representation with simultaneous parametrization of all linear controllers that provide internal stability of the closed-loop system can be achieved in the simplest and most natural way by analysing the system shown in Fig. 3 - the so-called basic structure. Problems of choosing the parameter to meet some important design specifications, viz. a robust asymptotic tracking of the reference signal with disturbance and noise rejection are also considered and illustrated by two representative examples covering the area of continuous- and discrete-time systems.

15

A multi-model approach to Saint-Venant equations: A stability study by LMIs

75%

Dos Santos Martins V. , Rodrigues M. , Diagne M.

|

nr 3

539-550

EN

This paper deals with the stability study of the nonlinear Saint-Venant Partial Differential Equation (PDE). The proposed approach is based on the multi-model concept which takes into account some Linear Time Invariant (LTI) models defined around a set of operating points. This method allows describing the dynamics of this nonlinear system in an infinite dimensional space over a wide operating range. A stability analysis of the nonlinear Saint-Venant PDE is proposed both by using Linear Matrix Inequalities (LMIs) and an Internal Model Boundary Control (IMBC) structure. The method is applied both in simulations and real experiments through a microchannel, illustrating thus the theoretical results developed in the paper.

16

Observer-based controller design of time-delay systems with an interval time-varying delay

63%

Thuan M. V. , Phat V. N. , Trinh H.

International Journal of Applied Mathematics and Computer Science

|

2012

|

tom Vol. 22, no. 4

921-927

EN

This paper considers the problem of designing an observer-based output feedback controller to exponentially stabilize a class of linear systems with an interval time-varying delay in the state vector. The delay is assumed to vary within an interval with known lower and upper bounds. The time-varying delay is not required to be differentiable, nor should its lower bound be zero. By constructing a set of Lyapunov-Krasovskii functionals and utilizing the Newton-Leibniz formula, a delay-dependent stabilizability condition which is expressed in terms of Linear Matrix Inequalities (LMIs) is derived to ensure the closed-loop system is exponentially stable with a prescribed \alfa-convergence rate. The design of an observer based output feedback controller can be carried out in a systematic and computationally efficient manner via the use of an LMI-based algorithm. A numerical example is given to illustrate the design procedure.

17

Stabilność asymptotyczna według składowych i stabilność wykładnicza dodatnich dyskretnych układów liniowych niecałkowitego rzędu

63%

Kaczorek T. , Cimochowski R.

Pomiary Automatyka Kontrola

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2010

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tom R. 56, nr 5

414-417

PL

Podano podstawowe definicje i twierdzenia dotyczące dodatnich układów dyskretnych niecałkowitego rzędu oraz omówiono ich stabilność asymptotyczną. Podano warunki konieczne i wystarczające stabilności asymptotycznej według składowych i stabilności wykładniczej dodatnich układów dyskretnych niecałkowitego rzędu. Przedstawiono przykłady numeryczne ilustrujące problem stabilności asymptotycznej według składowych i stabilności wykładniczej.

EN

In positive systems inputs, state variables and outputs take only non-negative values. Examples of positive systems are industrial processes involving chemical reactors, heat exchangers and distillation columns, storage systems, compartmental systems, water and atmospheric pollution models. A variety of models having positive linear systems behaviour can be found in engineering, management science, economics, social sciences, biology and medicine, etc. Positive linear systems are defined on cones and not on linear spaces. Therefore, the theory of positive systems is more complicated and less advanced. The concept of positive fractional discrete-time linear systems has been introduced in [6] and the reachability and controllability to zero of positive fractional system has been investigated in [10]. In this paper the problem of the componentwise asymptotic stability and exponential stability of the positive fractional systems will be solved. The paper is organized as follows. In section 2 the basic definitions and theorems concerning the positive fractional systems are recalled and their asymptotic stability is discussed. The main result of the paper is presented in section 3 and 4. Necessary and sufficient conditions for the componentwise asymptotic stability and exponential stability of the positive fractional systems are established. The considerations are illustrated by numerical examples in section 5. The algorithm in MATLAB, which allows the test of the componentwise asymptotic stability and exponential stability of the positive fractional systems is presented. How does presented procedure work is step-by step described. In section 6 the relationship between the componentwise asymptotic stability and exponential stability is presented. Concluding remarks and open problems are given in section 7.

18

A variable structure observer for the control of robot manipulators

63%

Abdessameud A. , Khelfi M. F.

International Journal of Applied Mathematics and Computer Science

|

2006

|

tom Vol. 16, no 2

189-196

EN

This paper deals with the application of a variable structure observer developed for a class of nonlinear systems to solve the trajectory tracking problem for rigid robot manipulators. The analyzed approach to observer design proposes a simple design methodology for systems having completely observable linear parts and bounded nonlinearities and/or uncertainties. This observer is basically the conventional Luenberger observer with an additional switching term that is used to guarantee robustness against modeling errors and system uncertainties. To solve the tracking problem, we use a control law developed for robot manipulators in the full information case. The closed loop system is shown to be globally asymptotically stable based on Lyapunov arguments. Simulation results on a 3-DOF robot manipulator show the asymptotic convergence of the vectors of observation and tracking errors.

19

A multi-model approach to Saint-Venant equations: A stability study by LMIs

63%

Dos Santos Martins V. , Rodrigues M. , Diagne M.

International Journal of Applied Mathematics and Computer Science

|

2012

|

tom Vol. 22, no. 3

539-550

EN

This paper deals with the stability study of the nonlinear Saint-Venant Partial Differential Equation (PDE). The proposed approach is based on the multi-model concept which takes into account some Linear Time Invariant (LTI) models defined around a set of operating points. This method allows describing the dynamics of this nonlinear system in an infinite dimensional space over a wide operating range. A stability analysis of the nonlinear Saint-Venant PDE is proposed both by using Linear Matrix Inequalities (LMIs) and an Internal Model Boundary Control (IMBC) structure. The method is applied both in simulations and real experiments through a microchannel, illustrating thus the theoretical results developed in the paper.

20

Extended Lie algebraic stability analysis for switched systems with continuous-time and discrete–time subsystems

63%

Zhai G. , Xu X. , Lin H. , Liu D.

|

tom Vol. 17, no 4

447-454

EN

We analyze stability for switched systems which are composed of both continuous-time and discrete-time subsystems. By considering a Lie algebra generated by all subsystem matrices, we show that if all subsystems are Hurwitz/Schur stable and this Lie algebra is solvable, then there is a common quadratic Lyapunov function for all subsystems and thus the switched system is exponentially stable under arbitrary switching. When not all subsystems are stable and the same Lie algebra is solvable, we show that there is a common quadratic Lyapunov-like function for all subsystems and the switched system is exponentially stable under a dwell time scheme. Two numerical examples are provided to demonstrate the result.