Robustness Check of the Stability of the Uncertain Vibration Control Systems with Interval Method

Variations in system parameters due to uncertainties may result in system performance deterioration. Uncertainties in modeling of structures are often considered to ensure that control system is robust with respect to parameter errors. The paper discusses the robustness check of the stability of vibration control systems with uncertain parameters. The uncertain parameters are described by interval variables. The uncertain property matrices are constructed directly using system physical parameters and avoided to use bounds in Euclidean norm. The feedback gain matrix is determined based on the deterministic systems with independent modal space control(IMSC), and then it is applied to the actual uncertain systems. A method to calculate the upper and lower bounds of eigenvalues of the closed-loop system with uncertain parameters is presented. The lower bounds of eigenvalues can be used to check the robustness of the stability of the controlled system with uncertain parameters.