Observer-based robust model predictive control of singular systems

Abstract

The robust model predictive control problem is studied for the singular systems with norm-bounded uncertainties when the states of controlled systems are immeasurable. By constructing the Lyapunov function with the error terms, the observer-based feedback control law is calculated by minimising the worst-case linear quadratic objective function. At each sampling time, the sufficient conditions for the existence of robust model predictive control are derived and expressed as linear matrix inequalities. It is proved that the robust stability of the closed-loop singular systems is guaranteed when the obtained feedback controller satisfies some conditions, and the regular and the impulse-free of the singular systems are also guaranteed. A simulation example is give to illustrate the efficiency of this method.