mu-Analysis and synthesis based on parameter dependent multipliers

It is well known that the structured singular value mu plays a crucial role in analysis and synthesis of the systems having structured uncertainties. In this paper, first, we propose new upper bounds of mu based on the parame ter dependent multipliers, which are less conservative than former ones. Se cond, using this type of multipliers, we give a necessary and sufficient co ndition for dynamical systems to have mu less than a specified value gamma for every frequency, which requires neither frequency sweep nor higher orde r multipliers. Third, based on this result, we solve a state feedback mu sy nthesis problem via LMI's. Numerical examples demonstrate the effectiveness of the proposed method.