Study on robust stability inverse problem for linear systems

Most of traditional robust problems focus on developing a robust controller to stabilize the dynamic system when system parameters perturb in certain bounded range. However, this paper studies the robust inverse problem, that is to say studying robust stability´s inverse problem (RSIP) for linear systems. In other words, it needs to find at least a stable system parameters´ perturbation space (SSPPS) for any given stable controller. A robust stability´s inverse theorem is proposed for linear systems, and SSPPS of stable controllers can be determined by inverse theorem. SSPPS is investigated by inverse theorem when system parameters appear perturbations. Numerical example and results are shown correctness and effectiveness of robust stability´s inverse theorem.