Nonlinear Vibrations, Stability Analysis, and Control

Solution and stability analysis of coupled nonlinear Schrodinger equations

We consider a new type of integrable coupled nonlinear Schrodinger (CNLS)equations proposed by our self [submitted to Phys. Plasmas (2011)]. The explicitform of soliton solutions are derived using the Hirota's bilinear method.We show that the parameters in the CNLS equations only determine the regionsfor the existence of bright and dark soliton solutions. Finally, throughthe linear stability an...

Uniform stability of damped nonlinear vibrations of an elastic string

Abstract. Here we are concerned about uniform stability of damped nonlinear transverse vibrations of an elastic string fixed at its two ends. The vibrations governed by nonlinear integro-differential equation of Kirchoff type, is shown to possess energy uniformly bounded by exponentially decaying function of time. The result is achieved by considering an energy-like Lyapunov functional for the ...

Nonlinear Phenomena and Stability Analysis for Discrete Control Systems

Stability Analysis of Nonlinear Parametric and Coulomb Control Systems

Stability analysis of nonlinear control systems using Lypunov’s direct method is reported in this paper. A general nonlinear controlled system and two different types of controllers are examined for stability analysis. The first category is the parametric controller. Importance of parametric controllers is illustrated through examples of various engineering systems. A general control algorithm ...

Nonlinear Control and Chaotic Vibrations of Perturbed Trajectories of Manipulators

We study different types of manipulators’ attractors and propose a motion control method. In our analysis the manipulator’s motion is perturbed and its stability investigated using the nonlinear equations of perturbations and linearized equations for practical control. In order to realize a practical control the common areas of stability for nonlinear and linear models are identified. The maps ...