Observer-based robust predictive control of singular systems with polytopic uncertainties

An observer-based robust predictive control algorithm for singular systems with convex polytopic uncertainties is presented by linear matrix inequality formulation. By constructing the Lyapunov function with the error term, the infinite time domain dasiamin-maxpsila optimization problems are converted into linear programming problems, the sufficient conditions for the existence of observer-based robust predictive control are obtained by linear matrix inequalities. It is proved that the robust stability of the closed-loop singular systems is guaranteed by the initial feasible solutions of the optimization problems, and the regular and the impulse-free of singular systems are also hold. A simulation example illustrates the efficiency of this method.