Quadratic guaranteed cost and disc pole location control for discrete-time uncertain systems

The paper deals with quadratic guaranteed cost control with pole placement in a disk. The objective is twofold: first to translate to discrete-time systems previous results for continuous-time systems. It is shown that in the two cases (discrete and continuous time), the procedures to design a state feedback control which places the poles in a disc and ensures a performance level through a linear quadratic criterion are formally identical. It consists of solving an optimisation problem. The second important point is to show that the criterion in this optimisation problem is convex with respect to epsilon and then a global optimal solution is reachable by a one-line search algorithm.