## 1 Introduction  
A passive tuned mass damper (TMD) [1; 2; 3] and active mass damper/driver (AMD) [4; 5; 6] are used to control the dynamic response of highly flexible buildings that are horizontally situated under a strong load, e.g., wind and earthquake. Indeed, the application of TMD is more extensive than AMD. Theoretically, the performance of an AMD control system is better than other forms of systems [7]. However, the negative influence of time-delay, which results in performance degradation and even in the instability of the system, limits its development and practical application [8; 9]. A time-delay effect mainly stems from the actuator response, which is primarily caused by a Control-Structure Interaction (CSI) effect, which exists between any type of structural active control system and its target structures. Therefore, the influence of the CSI effect on an AMD control system should be carefully considered when designing such a system [10; 11; 12; 13]. The actuator response time-delay is due to negative phases existing in the transfer function from control voltage to control force, but the influence of the frequency of control voltage on its phase (corresponding to actuator response time-delay) has often been neglected. Obviously, the actuator response time-delay induced by the CSI effect is affected by the sensitivity of the actuators, which is largely dependent on the drive mode. An electromagnetic drive is one of the most common forms in AMD control systems [14; 15],and the influence of the CSI effect on such systems needs to be focused on. In addition to these above references, the research on the CSI effect mainly concentrates on its influence on the control effect of control systems [16; 17; 18], or the impact of the CSI effect on structural dynamics [19]. Indeed, the structural dynamics are coupled with the performance of an AMD system with a CSI effect, and its performance is mainly connected with control gains. Meanwhile, different dynamical behaviors of civil engineering structures may result from structural parametric uncertainties [20]. However, the influences of control gains and uncertainties on the CSI effect remain unknown. In order to achieve a higher performance of an AMD system with a CSI effect, it is necessary to investigate the influencing factors of the CSI effect, including the input frequencies of control voltage, structural parametric uncertainties, and control gains. After analyzing such factors, several measures can be obtained to reduce this effect. In addition, to further solve the CSI problem, a suitable compensation control strategy is needed. Firstly, a Linear Quadratic Regulator (LQR) is a common control strategy for high-rise buildings [21], but it requires an accurate mathematical model. As a parameter perturbation or time-varying delay exists in a control system using LQR, its expected performance and stability are difficult to guarantee [22]. At present, the Linear Matrix Inequality (LMI) [23] approach is widely applied to analyze the stability of time-delay systems [24; 25] or design a Hoo time-delay compensation controller [26; 27]. However, Hoo control mainly considers the robust stability of the system by sacrificing its performance. To overcome this difficulty, a Guaranteed Cost Control (GCC) algorithm is proposed as a special LQR control method [28; 29]. In order to successfully apply the GCC algorithm for a high-rise building with an AMD control system, a key step involves solving a positive-definite solution of Riccati matrix equations. Previously, this problem has been based on the Riccati equation method, whose convergence cannot be guaranteed [30; 31]. However, an LMI approach can overcome this difficulty [32]. Several above References [10; 11; 12; 13] also indicate that classical algorithms cannot be effectively applied to eliminate the negative influence of a higher-order CSI effect. Therefore, in view of the structural parametric uncertainties and time-varying delays caused by a higher-order CSI effect, a new time-delay compensation controller is needed.