Non-minimal factorization approach to the -gain of discrete-time linear systems

A method is presented to compute the ℓ ∞ -gain of discrete-time linear MIMO systems which is based on a newly derived sequence of factorizations for G ( z ) . By resorting to a chain-scattering representation of the system, the proposed approach offers a criterion enabling one to cope with the static output feedback ℓ 1 -control design by solving a finite set of linear inequalities. Numerical examples are reported as well as an application to the synthesis of a performing decentralized ℓ 1 -controller.