Abstract: The finite time control problem was studied based on the state-feedback control for an uncertain linear singular system with exogenous disturbance, of which the state matrix and input matrix have norm-bounded uncertainties. By the Lyapunov functional method and linear matrix inequality (LMI) technique, the sufficient conditions of finite time boundedness (FTB) for the singular system via state feedback controller were provided. Then, the conditions were reduced to feasibility problems involving linear matrix inequalities (LMIs). Finally, a numerical example was given to illustrate the validity of this proposed method.

Key words: time-varying exogenous disturbance , linear matrix inequality (LMI), uncertain singular system, finite time boundedness (FTB)