Abstract: Highlights•Bounds a nonlinear system’s small-signal L2<math><msub is="true"><mrow is="true"><mi mathvariant="script" is="true">L</mi></mrow><mrow is="true"><mn is="true">2</mn></mrow></msub></math> gain in a subset of the state-space, Ω<math><mi is="true">Ω</mi></math>.•Finds an PI set in Ω<math><mi is="true">Ω</mi></math> that is robust to input disturbances in an L∞<math><msub is="true"><mrow is="true"><mi mathvariant="script" is="true">L</mi></mrow><mrow is="true"><mi is="true">∞</mi></mrow></msub></math> ball.•Algorithms bounding the gain and disturbance threshold use only convex optimization.•Rigorous verification of the local gain and small-signal requirement.
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