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The problem of robust model predictive control is studied for the singular systems with norm-bounded uncertainties when the states of controlled systems are unmeasurable. A new method is proposed by the observer-based feedback control. At each sampling time, the infinite time domain rdquomin-maxrdquo optimization problems are converted into convex optimization problems. By constructing the Lyapunov function with the error term, the sufficient conditions for the existence of robust model predictive control are derived and expressed as linear matrix inequalities. When the obtained feedback control satisfying some conditions, the robust stability of the closed-loop singular systems is guaranteed by the proposed design method, and the regular and the impulse-free of singular systems are also maintained. A simulation example illustrates the efficiency of this method.