Robust Stabilization for Parametric Uncertainty with Application to Magnetic Levitation
This paper considers the quadratic stabilization for a class of uncertain linear systems. The system under consideration contains norm-bounded time-varying uncertainties. The quadratic stability problem for the system is reduced to finding a common positive definite solution of 2 m Lyapunov equations, where m is the number of uncertain scalar parameters. A sufficient condition for the quadratic stabilizability of uncertain systems is derived in terms of a Riccati equation containing at most 2(m + 1) free parameters. The results are applied to the stabilizing control of a magnetic levitation system. The effectiveness of our method is illustrated both in simulations and experiments.
Key wordsquadratic stability quadratic stabilization Riccati equation magnetic levitation
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