An improved approach to robust stability analysis and controller synthesis for LPV systems

This paper revisits the problem of robust stability analysis and synthesis for linear parameter varying (LPV) systems. By introducing two new slack variables, new conditions for the polyquadratic stability and for the affine quadratic stability of LPV systems are presented in terms of linear matrix inequalities. These results are then applied for robust controller synthesis. Owing to the extra freedom degree introduced by the real slack variable, this proposed approach could lead to less conservative results than that of from the literature, especially for robust controller synthesis. The effectiveness and superiority are demonstrated by the comparison between this proposed approach and the existing results on a well‐known numerical example.