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Abstract. Stabilization of the system of wave equations coupled in parallel with coupling distributed springs and viscous dampers are under investigation due to different boundary conditions and wave propagation speeds. Numerical computations are attempted to confirm the theoretical results.2000 Mathematics Subject Classification. 58J45, 93D15, 93D20, 37D99, 35L05. 1.Introduction. Many problems in structural dynamics deal with stabilizing the elastic energy of partial differential equations by boundary or internal energy dissipative controllers for wave equations or the Euler-Bernoulli beam equation. Exponential stability is a very desirable property for such elastic systems. The energy multiplier method [2,6] has been successfully applied to reach to this objective for various partial differential equations and boundary conditions. Stabilization properties of serially connected vibrating strings or beams can be found in several papers [4,5]. There, uniform stabilization can be achieved if we employ dissipative boundary condition at one end. If otherwise, one damper is located at the mid-span joint of two vibrating strings coupled in series, the uniform stabilization property holds if c 1 /c 2 (wave speeds) has certain rational values. Stabilization properties of parallel connected vibrating strings were investigated under various end conditions by [9]. What comes new in this work is, firstly, dealing with the system of wave equations coupled in parallel with distributed viscous damping and springs (suspension system), and secondly, the rate of convergence of the solution when this system goes under the movement by an external disturbance (forcing function) or initial conditions. Having considered this, we are willing to furnish the best possible configuration that guarantees the uniform exponential stability due to different boundary conditions and wave speeds.Let Ω 1 = Ω 2 = Ω = (0, 1) be open sets in R. Also, let ∂Ω 1 ,∂Ω 2 be the boundaries of Ω 1 and Ω 2 , respectively. Throughout, (·) = d()/dt, ( ) = d()/dx, and ∂

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vious advantages.Two-time-scale (TTS) distributions are introduced. For a class of stable systems, it is shown that every TTS distribution has a two-frequency-scale (TFS) Laplace transform. Conversely, it is shown that the impulse response of any stable TFS transfer function, and hence any stable (standard) singularly perturbed system, can be characterized in terms of a stable TTS distribution. A time domain decomposition for TTS distributions is obtained which parallels the slow and fast decompositions of singularly perturbed systems and also the frequency domain decompositions of TFS transfer functions. It is shown that every stable TTS

Abstract-The centralized control of large scale systems is usually infeasible due to their high dimensionality, nonlinearity, coupling, time delay and etc. In order to overcome the mentioned difficulties, this paper presents an application of decentralized fuzzy logic controller (FLC) which is optimum by Simulated Annealing (SA) algorithm on two interconnected power area for the load frequency control as a case study of large scale systems. The simulation study is undertaken, based on MATLAB / SIMULINK to demonstrate and confirm the effectiveness of proposed method.Index Terms-Fuzzy logic control; simulated annealing optimization method, large scale systems; load frequency control.

Analytical approximate solutions of Duffing and Van der Pol equations as well as the system of coupled Euler-Bernoulli beams and wave equations are under consideration. To this end, the Adomian Decomposition Method (ADM) and variational iteration method (VIM) have been employed to obtain analytical solutions to these differential equations. The results are compared with accurate numerical computations, which show that ADM is a high performance and accurate method to use for the analytical solution of nonlinear physical problems.