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

Tom R.V. Steentjes; Alina I. Doban; Mircea Lazar

doi:10.1016/j.ifacol.2016.10.132

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

Tom R.V. Steentjes, Alina I. Doban, Mircea Lazar

Research output: Contribution to journal › Conference article › peer-review

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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 language	English
Pages (from-to)	13-18
Journal	IFAC-PapersOnLine
Volume	49
Issue number	18
DOIs	https://doi.org/10.1016/j.ifacol.2016.10.132
Publication status	Published - 2016
Event	10th IFAC Symposium on Nonlinear Control Systems (NOLCOS 2016), August 23-25, 2016, Monterey, Cal., USA - Monterey, United States Duration: 23 Aug 2016 → 25 Aug 2016

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10.1016/j.ifacol.2016.10.132

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@article{65e2369a60b948afa5c20fd06269fe43,

title = "Construction of continuous and piecewise affine Lyapunov functions via a finite-time converse",

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.",

author = "Steentjes, {Tom R.V.} and Doban, {Alina I.} and Mircea Lazar",

year = "2016",

doi = "10.1016/j.ifacol.2016.10.132",

language = "English",

volume = "49",

pages = "13--18",

journal = "IFAC-PapersOnLine",

issn = "2405-8963",

publisher = "Elsevier",

number = "18",

note = "10th IFAC Symposium on Nonlinear Control Systems (NOLCOS 2016), August 23-25, 2016, Monterey, Cal., USA, NOLCOS 2016 ; Conference date: 23-08-2016 Through 25-08-2016",

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TY - JOUR

T1 - Construction of continuous and piecewise affine Lyapunov functions via a finite-time converse

AU - Steentjes, Tom R.V.

AU - Doban, Alina I.

AU - Lazar, Mircea

PY - 2016

Y1 - 2016

N2 - 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.

AB - 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.

U2 - 10.1016/j.ifacol.2016.10.132

DO - 10.1016/j.ifacol.2016.10.132

M3 - Conference article

SN - 2405-8963

VL - 49

SP - 13

EP - 18

JO - IFAC-PapersOnLine

JF - IFAC-PapersOnLine

IS - 18

T2 - 10th IFAC Symposium on Nonlinear Control Systems (NOLCOS 2016), August 23-25, 2016, Monterey, Cal., USA

Y2 - 23 August 2016 through 25 August 2016

ER -

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

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