关键词: 工程力学, 参数不确定系统, 振动控制, 凸模型理论, 二阶摄动, 闭环系统特征值上下界

Abstract: By using the convex model theory, the vibration control problem of structures with uncertain parameters is discussed, which is approximated by a deterministic one. The uncertain parameters are modeled to be a convex elliptical set rather than a probabilistic set. This does not require the probabilistic distribution descriptions of the uncertain parameters. The feedback gain matrices derived from the deterministic systems are applied to the actual uncertain systems, and a method for estimating the upper and lower bounds of the real and imaginary parts of eigenvalues of the closedloop systems is presented by combining the secondorder matrix perturbation and optimization. The numerical results show that the present method is effective.

Key words: engineering mechanics, uncertain parameters systems, vibration active control, convex model, secondorder matrix perturbation, upper and lower bounds of eigenvalues of the closedloop systems