lth-Step Lyapunov Min-Max Controllers: Stabilizing Discrete-Time Systems under Real Parameter Variations

In this paper we are concerned with the stability robustness of discrete-time systems which experience real, structured, parameter variations. The work is motivated by the notion of a "Lyapunov min-max controller" introduced by Corless [13]. We generalize this concept and introduce lth-step Lyapunov min-max controllers. With the help of these controllers we are able to identify a class of structured uncertainties, appropriately called "lth-step matched uncertainties" for which we can guarantee asymptotic stability. These structures include the so-called "matched uncertainties" as a special case.