μ-analysis and synthesis of state feedback systems based on multipliers and LMI´s

This paper provides a μ analysis and synthesis method of state feedback systems. First, we derive a sufficient condition for the dynamical system to have μ less than a specified value γ by using parameter-dependent multipliers and the positive real lemma. It requires no higher order multiplier and no frequency sweep while being less conservative than former methods. Second, based on this result, we give an LMI condition for the existence of a state feedback gain which achieves that μ of the closed loop system is less than given γ. Finally, an illustrative numerical example is given.