Constrained interpolation-based control for polytopic uncertain systems

In this paper, we consider the regulation problem for uncertain and time-varying linear discrete-time systems with bounded input and bounded state. By using an interpolation technique it is shown that, the convex hull of a set of invariant ellipsoids is also invariant. Feasibility and robustly and asymptotically stable closed-loop behavior are assured by minimizing an appropriate objective function. Moreover we show that the control value can be computed by solving nonlinear equations.