On peak effects in discrete time linear systems

It is well known that input-free stable linear systems with nonzero initial conditions may experience large deviations of the trajectory from the origin prior to converging to zero. Analysis of the transients of discrete-time systems is the subject of this paper. Simple LMI-based upper bounds on deviations are presented, and the same-flavor stabilizing feedback design procedure aimed at minimizing the peak is discussed. For companion-form systems, lower bounds are proposed for specific initial conditions; peaking effects for the norms of powers of Schur stable matrices are also analyzed.