Displaying similar documents to “Exponential stability of a flexible structure with history and thermal effect”

Around certain critical cases in stability studies in hydraulic engineering

Vladimir Răsvan (2023)

Archivum Mathematicum

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It is considered the mathematical model of a benchmark hydroelectric power plant containing a water reservoir (lake), two water conduits (the tunnel and the turbine penstock), the surge tank and the hydraulic turbine; all distributed (Darcy-Weisbach) and local hydraulic losses are neglected,the only energy dissipator remains the throttling of the surge tank. Exponential stability would require asymptotic stability of the difference operator associated to the model. However in this case...

Non-exponential and polynomial stability results of a Bresse system with one infinite memory in the vertical displacement

Aissa Guesmia (2017)

Nonautonomous Dynamical Systems

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The asymptotic stability of one-dimensional linear Bresse systems under infinite memories was obtained by Guesmia and Kafini [10] (three infinite memories), Guesmia and Kirane [11] (two infinite memories), Guesmia [9] (one infinite memory acting on the longitudinal displacement) and De Lima Santos et al. [6] (one infinite memory acting on the shear angle displacement). When the kernel functions have an exponential decay at infinity, the obtained stability estimates in these papers lead...

Exponential stability of nonlinear non-autonomous multivariable systems

Michael I. Gil' (2015)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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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...

Exponential stability of distributed parameter systems governed by symmetric hyperbolic partial differential equations using Lyapunov’s second method

Abdoua Tchousso, Thibaut Besson, Cheng-Zhong Xu (2009)

ESAIM: Control, Optimisation and Calculus of Variations

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In this paper we study asymptotic behaviour of distributed parameter systems governed by partial differential equations (abbreviated to PDE). We first review some recently developed results on the stability analysis of PDE systems by Lyapunov’s second method. On constructing Lyapunov functionals we prove next an asymptotic exponential stability result for a class of symmetric hyperbolic PDE systems. Then we apply the result to establish exponential stability of various chemical engineering...

Controlling Nanoparticles Formation in Molten Metallic Bilayers by Pulsed-Laser Interference Heating

M. Khenner, S. Yadavali, R. Kalyanaraman (2012)

Mathematical Modelling of Natural Phenomena

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The impacts of the two-beam interference heating on the number of core-shell and embedded nanoparticles and on nanostructure coarsening are studied numerically based on the non-linear dynamical model for dewetting of the pulsed-laser irradiated, thin (< 20 nm) metallic bilayers. The model incorporates thermocapillary forces and disjoining pressures, and assumes dewetting from the optically transparent substrate atop of the reflective...

On exponential stability of second order delay differential equations

Ravi P. Agarwal, Alexander Domoshnitsky, Abraham Maghakyan (2015)

Czechoslovak Mathematical Journal

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We propose a new method for studying stability of second order delay differential equations. Results we obtained are of the form: the exponential stability of ordinary differential equation implies the exponential stability of the corresponding delay differential equation if the delays are small enough. We estimate this smallness through the coefficients of this delay equation. Examples demonstrate that our tests of the exponential stability are essentially better than the known ones....