7 L2 Gain 7.1 L2 Gain for Behavioral Models

7.1.1 L2 Gain for Continuous Time Signals Let S be a behavioral model of a continuous time system (i.e. S is a subset of the set L of all n-dimensional signals – locally square integrable functions v : [0,∞) 7→ R. Let Lw and Le be two fixed real matrices of dimension m-by-n and k-by-n respectively. For every v ∈ S, equalities w = Lwv and e = Lev define two signals w and e which can be viewed as ”components” of v. The L2 gain of S from input w to output e is defined as the maximal lower bound for γ ≥ 0 such that