In recent years, Sum–Of–Squares (SOS) method has attracted increasing interest as a new approach for stability analysis and controller design of nonlinear dynamic systems. This paper utilizes SOS method to design a robust nonlinear controller for longitudinal dynamics of a hypersonic aircraft model. Specifically, the searching of the nonlinear robust controller is reformulated as a robust SOS/robust LMI problem, and then solved via a stochastic iterative algorithm. As the simulation results show, the designed controller is capable of stabilizing the aircraft and following pilot commands in presence of parametric uncertainties in the aircraft model.

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