Abstract
This paper considers the quadratic stabilization for a class of uncertain linear systems. The system under consideration contains norm-bounded time-varying uncertainties which linearly depends on scalar parameters. The quadratic stability problem for the system is reduced to finding a common positive definite solution of 2m Lyapunov inequalities, where m is the number of uncertain scalar parameters. We derive a sufficient condition for the quadratic stabilizability of the uncertain system in terms of a Riccati equation containing 2(m+1) free parameters. The results are applied to the stabilizing control of a magnetic levitation system. The effectiveness of our methods is illustrated both in simulations and experiments.
