Robust stabilization of infinite dimensional systems by finite dimensional controllers |
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| Authors: | Ruth F. Curtain Keith Glover |
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| Affiliation: | 1. College of Automation and Electronic Engineering, Qingdao University of Science and Technology, Qingdao 266061, PR China;2. Graduate School of Engineering, Tokyo University of Agriculture and Technology, 2-24-16 Nakacho, Koganei, Tokyo 184–8588, Japan;1. Max Planck Institute for Dynamics of Complex Technical Systems, Sandtorstr. 1, 39106 Magdeburg, Germany;2. Faculty of Mathematics, Otto von Guericke University Magdeburg, Universitätsplatz 2, 39106 Magdeburg, Germany;1. School of Mathematics and Statistics Science, Ludong University, Yantai, Shandong 264025, China;2. Department of Mechanical Engineering, Politecnico di Milano, Milan 20156, Italy |
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| Abstract: | The problem of robustly stabilizing an infinite dimensional system with transfer function G, subject to an additive perturbation Δ is considered. It is assumed that: G ε 0(σ) of systems introduced by Callier and Desoer [3]; the perturbation satisfies |W1ΔW2| < ε, where W1 and W2 are stable and minimum phase; and G and G + Δ have the same number of poles in +. Now write W1GW2=G1 + G1, where G1 is rational and totally unstable and G2 is stable. Generalizing the finite dimensional results of Glover [12] this family of perturbed systems is shown to be stabilizable if and only if ε σmin (G*1)( = the smallest Hankel singular value of G*1). A finite dimensional stabilizing controller is then given by where 2 is a rational approximation of G2 such that ) and K1 robustly stabilizes G1 to margin ε. The feedback system (G, K) will then be stable if |W1ΔW2| ∞< ε − Δ. |
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| Keywords: | Infinite dimensional systems Robust stabilization Model approximation |
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