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

A method is presented to compute the ℓ∞ℓ∞-gain of discrete-time linear MIMO systems which is based on a newly derived sequence of factorizations for G(z)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 ℓ1ℓ1-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 ℓ1ℓ1-controller.