On the ℓ∞-gain computation of linear time-varying SISO systems

The problem of the ℓ_∞-gain computation of BIBO-stable SISO linear time-varying systems is considered. Based on a factorization of the rational representation of the system, a sequence approximating the sought ℓ_∞-gain is constructed. The proposed algorithm requires one polynomial factorization only and the computation of the ℓ_∞-gain of a sequence of finite impulse response subsystems whose rational representation is provided through a closed form formula. The general methodology is illustrated with a numerical example.