Boundary feedback stabilization of a flexible wing model under unsteady aerodynamic loads

This paper addresses the boundary stabilization of a flexible wing model, both in bending and twisting displacements, under unsteady aerodynamic loads, and in presence of a store. The wing dynamics is captured by a distributed parameter system as a coupled Euler-Bernoulli and Timoshenko beam model. The problem is tackled in the framework of semigroup theory, and a Lyapunov-based stability analysis is carried out to assess that the system energy, as well as the bending and twisting displacements, decay exponentially to zero. The effectiveness of the proposed boundary control scheme is evaluated based on simulations.Comment: Published in Automatica as a brief pape

Interior feedback stabilization of wave equations with dynamic boundary delay

In this paper we consider an interior stabilization problem for the wave equation with dynamic boundary delay.We prove some stability results under the choice of damping operator. The proof of the main result is based on a frequency domain method and combines a contradiction argument with the multiplier technique to carry out a special analysis for the resolvent

Asymptotic stability and blow up for a semilinear damped wave equation with dynamic boundary conditions

In this paper we consider a multi-dimensional wave equation with dynamic boundary conditions, related to the Kelvin-Voigt damping. Global existence and asymptotic stability of solutions starting in a stable set are proved. Blow up for solutions of the problem with linear dynamic boundary conditions with initial data in the unstable set is also obtained

Efficient Reorientation Maneuvers for Spacecraft with Multiple Articulated Payloads

A final report is provided which describes the research program during the period 3 Mar. 1992 to 3 Jun. 1993. A summary of the technical research questions that were studied and of the main results that were obtained is given. The specific outcomes of the research program, including both educational impacts as well as research publications, are listed. The research is concerned with efficient reorientation maneuvers for spacecraft with multiple articulated payloads

A robust LMI approach on nonlinear feedback stabilization of continuous state-delay systems with Lipschitzian nonlinearities : experimental validation

This paper suggests a novel nonlinear state-fe edback stabilization control law using linear matrix inequalities for a class oftime-delayed nonlinear dynamic systems with Lipschitz nonlinearity conditions. Based on the Lyapunov–Krasovskiistability theory, the asymptotic stabilization criterion is derived in the linear matrix inequality form and the coef¿cients ofthe nonlinear state-feedback controller are determined. Meanwhile, an appropriate criterion to ¿nd the proper feedbackgain matrix F is also provided. The robustness purpose against nonlinear functions and time delays is guaranteed in thisscheme. Moreover , the problem of robust H!performance analysis for a class of nonlinear time-delayed system s withexternal disturbance is studied in this paper. Simulations are presented to demonstrate the pro¿ciency of the offeredtechnique. For this purpos e, an unstable nonlinear numerical system and a rotary inverted pendulum system have beenstudied in the simulation section. Moreover, an experimental study of the practical rotary inverted pendul um system isprovided. These results con¿rm the expected satisfactory performance of the suggested method.Peer ReviewedPostprint (author's final draft

Stability analysis of laminated beam systems with delay using lyapunov functional

This work is concerned with systems of laminated beams model subject to linear and nonlinear delay feedback. In a dynamic laminated beam, time delay manifests in the form of lags in restoring the desired system stability after perturbations. Four prevalent categories of time delay are considered. For laminated beams with relatively high adhesive stiffness, a constant delay feedback is considered for systems made up of individual beams with same elasticity, and neutral delay otherwise. In systems where delay is significantly due to adhesive softening, distributed delay is considered. Lastly, in structures where the mechanism of dissipating energy is nonlinear, a corresponding nonlinear delay effect is investigated. The mechanism of stabilization mainly relies on the intrinsic structural damping, unlike in previous works where researchers introduced additional dampings such as boundary feedback and material damping. The objective of this work is to establish the asymptotic behavior of a vibrating Timoshenko laminated beam using structural or utmost a single frictional damping in presence of different forms of time delay. The energy method for partial differential equations is the main tool used to establish wellposedness results and asymptotic behavior. The existence and uniqueness of the solution is proved using the linear semi group theory, whereas for energy decay properties, the multiplier technique involving constructing a suitable Lyapunov functional equivalent to the energy is utilized. With appropriate assumptions on the delay weight and wave speeds, it is established that the energy of the system at least decays exponentially due to structural damping. Furthermore, a single additional frictional damping guarantees polynomial decay despite the presence of constant or distributed delay feedback. For nonlinear structural damping, with help of some convexity arguments, general decay result is achieved. In summary, depending on the damping mechanism(s), exponential, polynomial, or general decay results of a laminated beam system subject to different forms of delay feedback are established

General decay of the solution for a viscoelastic wave equation with a time-varying delay term in the internal feedback

In this paper we consider a viscoelastic wave equation with a time-varying delay term, the coefficient of which is not necessarily positive. By introducing suitable energy and Lyapunov functionals, under suitable assumptions, we establish a general energy decay result from which the exponential and polynomial types of decay are only special cases.Comment: 11 page