Construction of continuous and piecewise affine Lyapunov functions via a finite-time converse

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Abstract

A novel numerical Massera-type approach for the computation of Lyapunov functions (LFs) for nonlinear continuous-time systems is presented. The construction is enabled by verifying a finite-time decrease condition for a candidate function, which is allowed to be any K∞ function of the norm of the state, and applying a converse Lyapunov theorem. In the construction we make use of approximated system trajectories and we obtain a continuous and piecewise affine (CPA) LF. By optimization, the obtained CPA LF is verified and an estimate of the domain of attraction is obtained. Several examples are presented for illustration and demonstration of the effectiveness of the proposed approach.
Original languageEnglish
Pages (from-to)13-18
JournalIFAC-PapersOnLine
Volume49
Issue number18
DOIs
Publication statusPublished - 2016
Event10th IFAC Symposium on Nonlinear Control Systems (NOLCOS 2016), August 23-25, 2016, Monterey, Cal., USA - Monterey, United States
Duration: 23 Aug 201625 Aug 2016

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