Finite-Time Vibration-Attenuation Controller Design for Structural Systems with Parameter Uncertainties

Abstract

The problem of finite-time vibration-attenuation controller design for buildings structural systems with parameter uncertainties is the concern of this paper. The objective of designing controllers is to guarantee the finite-time stability of closed-loop systems with a prescribed level of disturbance attenuation. First, based on matrix transformation, the structural system is described as state-space model, which contains parameter uncertainties. Then, based on finite-time stability analysis method, some sufficient conditions for the existence of finite-time vibration-attenuation controllers are obtained. By solving these conditions, the desired controllers can be obtained for the closed-loop system to be finite-time stable with the performance ‖ ‖ 2 < ‖ ‖ 2 . It is shown by the simulation results, that compared with some Lyapunov asymptotic stability results, finite-time stability control can obtain better state responses, especially while the system is under nonzero initial states.

Novel Stabilization Conditions for Uncertain Singular Systems with Time-Varying Delay

“…This section is concluded by presenting a lemma, which will be used in the proof of our main results. Lemma 4 (see [30,31]). Given matrices , , and ] with appropriate dimensions and with symmetrical, then +…”

Acceleration-Based Vibration Control for Structural Systems with Actuator Faults and Finite-Time State Constraint

“…By pre and post-multiplying (9) with diag { P -1 I } and its transpose, we can obtain (13) From (12) and (13), it is easy to obtain . (14) After doing the same operation as those in [22], we can obtain x T ( t ) Rx ( t )<k 2 2 and ||z|| 2 <g||w|| 2 from the conditions (7)- (8). From Definition 1, we know the system is finite-time state-constraint H ∞ stabilizable with respect to (k 1 ,k 2 , R,T,g,d ).…”

“…we solve the LMIs (6)- (8), and obtain a state feedback controller which has the following gain matrix For description in brevity, we denote this designed controller as controller I thereafter. In order to facilitate the comparison, we obtain an non-acceleration-based controller by solving the Theorem 1 in [22] with g=0.1, a=0.1 and this controller has the following gain…”

“…Recently, the problem of finite-time stability of continuous and discrete systems has received considerable attention. For example, based on LMIs technique, the problem of finite-time vibration-attenuation controller design for buildings structural systems with parameter uncertainties is considered in [22]. Based on a Lyapunov functional, the problem of finitetime stabilization under asynchronous switching is dealt with in [23] for a class of switched time-delay systems with nonlinear disturbances.…”

Empirical multi-degree-of-freedom-generalized minimum variance control for buildings during earthquakes

“…[2][3][4][5][6][7][8] One of the important missions of structural control is to ensure the safety of structures and cities during large earthquakes. [9][10][11][12][13] In fact, Weng et al 14 have proposed the finite-time vibration control of earthquake-excited linear structures with input time-delay by considering the saturation. The objective of designing controllers is to guarantee the finite-time stability of closed-loop systems while attenuating earthquake-induced vibration of the structures.…”