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In this paper, we focus on the lower bounds of the L_p (p ∈ [1,∞), p = ∞) induced norms of continuous-time LTI systems where input signals are restricted to be nonnegative. This induced norm, called t...he L_<p+> induced norm, is particularly useful for the stability analysis of nonlinear feedback systems constructed from linear systems and static nonlinearities where the nonlinearities provide only nonnegative signals for the case p = 2. To have deeper understanding on the L_<p+> induced norm, we analyze its lower bounds with respect to the standard L_p induced norm in this paper. As the main result, we show that the L_<p+> induced norm of an LTI system cannot be smaller than the L_p induced norm scaled by 2^<(1-p)/p> for ∈ [1,∞) (scaled by 2^<−1> for p = ∞). On the other hand, in the case where p = 2, we further propose a method to compute better (larger) lower bounds for single-input systems via reduction of the lower bound analysis problem into a semi-infinite programming problem. The effectiveness of the lower bound computation method, together with an upper bound computation method proposed in our preceding paper, is illustrated by numerical examples.続きを見る
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