Elastic Stabilization Control for Polynomial Parameter-varying Systems with Applications to a Turbofan Engine

Aiming at the problem of the controller parameter perturbation and exponential stabilization of controlled plants in complex working environments, an elastic stabilization control method, which is based on polynomial parameter-varying (PPV) model is proposed. To address the parameter perturbation problem of controller in the controlled plants, the conditions for the existence of the elastic controller that ensures the exponential stability of the PPV systems are derived using Lyapunov stability theory and state-and-parameter-dependent (SPD) linear matrix inequalities. The controller is solved by using the sum of squares (SOS) convex optimization technique. Finally, the proposed method is applied to the control problem of PPV model of turbofan engine. The numerical simulation results show that the designed controller has good control performance, and is robust in the large envelope range of the engine.