On the characterization of extreme switching sequences

In this paper, we consider the problem of finding a switching sequence to minimize or maximize the norm of certain classes of linear switched systems in the sense of H
₂
, and induced l
_∞
or l
₁
norm. The motivation is to study certain types of model matching problems including filtering. In particular we show that, for FIR switching system models and induced l
_∞
norms, the minimizing switching sequence can be chosen to be periodic.