This article investigates the problem of finite-time control for the mode transition of turbine-based combined cycle (TBCC) engines described in the polynomial parameter-varying (PPV) framework. In order to realize small-deviation mode transition, a PPV model that can be applied to different opening rates of an inlet splitter is established for a TBCC project put forward by Xiamen University named Xiamen Turbine-based Ejector Ramjet (XTER). The concepts of uniformly finite-time stability and uniformly finite-time output tracking performance are proposed, together with the corresponding state-and-parameter-dependent controller design conditions which can be efficiently solved by using sum-of-squares programming. Meanwhile, based on the PPV system of XTER, the controllers are designed in the designed flight conditions and the non-designed flight conditions, respectively. Finally, simulation results on the mode transition of the XTER are given to verify the feasibility and effectiveness of the proposed control scheme.
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