Mixed-μ analysis for dynamical systems using descriptor form

This paper provides a new mixed-μ analysis method for dynamical systems without the frequency sweep. First, we derive a necessary and sufficient condition for the closed loop system with dynamical system and real uncertainties to have μ less than a specified value γ by using descriptor form. Second, applying the sector transformation and the strictly positive real lemma to this result, we give a computable LMI condition in the state space for the mixed-μ analysis problem. The proposed method can treat all uncertainties as time invariant, and it may be less conservative than former ones including the D-G scaling. Finally, an illustrative numerical example is given