Robust stabilisation of polynomial systems with uncertain parameters

The last few years witnessed an increasing interest in the problem of control design of nonlinear systems. A special and very interesting class of nonlinear systems is those with polynomial vector fields. Moreover, the models of real physical systems usually contain uncertainties typically due to bad knowledge of the values of the parameters. This article presents a systematic computational procedure for the design of controllers for polynomial systems with uncertain parameters, combining some results of real algebraic geometry, polynomial certificates and recent numerical methods for verification of the positivity of polynomials. The applicability of the proposed approach is tested by numerical simulations including nonlinear oscillators with polynomial restoring forces with uncertain parameters.

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