Quantitative local L2-gain and Reachability analysis for nonlinear systems

Erin Summers, Abhijit Chakraborty, Weehong Tan, Ufuk Topcu, Pete Seiler, Gary Balas, Andrew Packard

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


This paper develops theoretical and numerical tools for quantitative local analysis of nonlinear systems. Specifically, sufficient conditions are provided for bounds on the reachable set and L2 gain of the nonlinear system subject to norm-bounded disturbance inputs. The main theoretical results are extensions of classical dissipation inequalities but enforced only on local regions of the state and input space. Computational algorithms are derived from these local results by restricting to polynomial systems, using convex relaxations, for example the S-procedure, and applying sum-of-squares optimizations. Several pedagogical and realistic examples are provided to illustrate the proposed approach.

Original languageEnglish (US)
Pages (from-to)1115-1135
Number of pages21
JournalInternational Journal of Robust and Nonlinear Control
Issue number10
StatePublished - Jul 10 2013


  • dissipation inequalities
  • local L gain
  • nonlinear systems
  • reachability
  • sum-of-squares polynomial


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