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This paper is concerned with the analysis of the $L_{2}$ induced norm ofcontinuous-time LTI systems where the input signals are restricted to benonnegative. This induced norm is referred to as the $L_{2+}$ induced norm inthis paper. It has been shown very recently that the $L_{2+}$ induced norm isparticularly useful for the stability analysis of nonlinear feedback systemsconstructed from linear systems and static nonlinearities where the nonlinearelements only provide nonnegative signals. For the upper bound computation ofthe $L_{2+}$ induced norm, an approach with copositive programming has alsobeen proposed. It is nonetheless true that this approach becomes effective onlyfor multi-input systems, and for single-input systems this approach does notbring any improvement over the trivial upper bound, the standard $L_2$ norm. Toovercome this difficulty, we newly introduce positive filters to increase thenumber of positive signals. This enables us to enlarge the size of thecopositive multipliers so that we can obtain better (smaller) upper bounds withcopositive programming.

$L_{2+}$ Induced Norm Analysis of Continuous-Time LTI Systems Using Positive Filters and Copositive Programming