{"paper":{"title":"Bode's Sensitivity Integral Constraints: The Waterbed Effect Revisited","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.SY","authors_text":"Abbas Emami-Naeini, Dick de Roover","submitted_at":"2019-01-09T17:49:21Z","abstract_excerpt":"Bode's sensitivity integral constraints define a fundamental rule about the limitations of feedback and is referred to as the waterbed effect. We take a fresh look at this problem and reveal an elegant and fundamental result that has been seemingly masked by previous derivations. The main result is that the sensitivity integral constraint is crucially related to the difference in speed of the closed-loop system as compared to that of the open-loop system. This makes much intuitive sense. Similar results are also derived for the complementary sensitivity function. In that case the integral cons"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.11302","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}