Robust ℋ∞ control for a class of nonlinear systems: a LMI approach

Considers the problem of robust ℋ_∞ control for a class of nonlinear systems. The nonlinear uncertainties which we allow include those satisfying integral quadratic constraints (IQCs), and those nonlinear bounded terms satisfying matching conditions. We adopt an LMI approach to designing a state feedback controller which guarantees the so-called L₂-gain from the exogenous input noise to the controlled output to be no larger than a prescribed value. We then extend this robust ℋ_∞ result to systems for which the nonlinear uncertainty satisfies generalized matching conditions