Ellipsoid bounds on state trajectories for discrete-time systems with time-invariant and time-varying linear fractional uncertainties

Polynomial-time algorithms are proposed for computing tight ellipsoidal bounds on the state trajectories of discrete-time linear systems with time-varying or time-invariant linear fractional parameter uncertainties and ellipsoidal uncertainty in the initial state. The approach employs linear matrix inequalities to determine an initial estimate of the ellipsoid, which is improved by the subsequent application of the skewed structured singular value. Tradeoffs between computational complexity and conservatism are discussed for the three algorithms. Small conservatism for the tightest bounds is observed in numerical examples used to compare the algorithms.