μ-Analysis and synthesis based on parameter dependent multipliers
It is well known that the structured singular value μ plays a crucial role in analysis and synthesis of the systems having structured uncertainties. In this paper, first, we propose new upper bounds of μ based on the parameter dependent multipliers, which are less conservative than former ones. Second, using this type of multipliers, we give a necessary and sufficient condition for dynamical systems to have μ less than a specified value γ for every frequency, which requires neither frequency sweep nor higher order multipliers. Third, based on this result, we solve a state feedback μ synthesis problem via LMI’s. Numerical examples demonstrate the effectiveness of the proposed method.
KeywordsState Feedback Synthesis Problem Small Gain Theorem Bilinear Matrix Inequality Suboptimal Controller
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