μ-Analysis and synthesis based on parameter dependent multipliers
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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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- M. Fu and N.E. Barabanov: Improved Upper Bounds of the Structured Singular Value, Proc. 34th IEEE CDC, 3115/3120(1995)Google Scholar
- T. Asai, S. Hara and T. Iwasaki: Simultaneous Modeling and Synthesis for Robust Control by LFT Scaling, Proc. IFAC World Congress, vol.G, 309–314(1996)Google Scholar
- G. Chen and T. Sugie: An Upper Bound of μ based on the Parameter Dependent Multipliers, Proc. 16th ACC, 2604/2608(1997)Google Scholar
- P. Gahinet, P. Apkarian, M. Chilali and E. Feron: Affine Parameter-Dependent Lyapunov Functions and Real Parameter Uncertainty, Proc. 3rd ECC, 2262/2267(1995)Google Scholar
- P. Gahinet, A. Nemirovski, A. J. Laub, M. Chilali: LMI Control Toolbox, MATH WORKS, 1995Google Scholar
- K. C. Goh, J. H. Ly, L. Turan and M. G. Safonov, μ/K m-Synthesis via Bilinear Matrix Inequalities, Proc. 33rd IEEE CDC, 2032/2037(1994)Google Scholar
- M. Kawanishi and T. Sugie: Design of μ Suboptimal Controllers based on S-procedure and Generalized Strong Positive Real Lemma, 35th IEEE CDC, 3525/3526(1996)Google Scholar
- M. G. Safonov, K. C. Goh and J. H. Ly: Control System Synthesis via Bilinear Matrix Inequalities, Proc. 14th ACC, 45/49(1994)Google Scholar