On the computation of Lyapunov functions for discrete–time nonlinear systems

R.V. Bobiti; M. Lazar

doi:10.1109/ICSTCC.2014.6982397

On the computation of Lyapunov functions for discrete–time nonlinear systems

R.V. Bobiti, M. Lazar

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

11 Citations (Scopus)

7 Downloads (Pure)

Abstract

This paper considers the problem of computing a Lyapunov function for nonlinear discrete–time systems. The proposed solution is systematic and consists of two steps. First, a pseudo–Lyapunov function, called finite–step Lyapunov function, is computed by solving a finite dimensional nonlinear optimization problem. Then, a recent converse theorem is employed, which gives an explicit construction of a Lyapunov function from a finite–step Lyapunov function. This procedure produces additionally an invariant set, through a nonlinear optimization program. An example illustrates the developed procedure and gives insight into the problem complexity

Original language	English
Title of host publication	Proceedings of the 18th International Conference on System Theory, Control and Computing (ICSTCC) 17-19 October 2014, Sinaia, Romania
Place of Publication	Piscataway
Publisher	Institute of Electrical and Electronics Engineers
Pages	93-98
DOIs	https://doi.org/10.1109/ICSTCC.2014.6982397
Publication status	Published - 2014
Event	18th International Conference on System Theory, Control and Computing, ICSTCC 2014 - Sinaia, Romania Duration: 17 Oct 2014 → 19 Oct 2014 Conference number: 18

Conference

Conference	18th International Conference on System Theory, Control and Computing, ICSTCC 2014
Abbreviated title	ICSTCC 2014
Country/Territory	Romania
City	Sinaia
Period	17/10/14 → 19/10/14

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10.1109/ICSTCC.2014.6982397

Cite this

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title = "On the computation of Lyapunov functions for discrete–time nonlinear systems",

abstract = "This paper considers the problem of computing a Lyapunov function for nonlinear discrete–time systems. The proposed solution is systematic and consists of two steps. First, a pseudo–Lyapunov function, called finite–step Lyapunov function, is computed by solving a finite dimensional nonlinear optimization problem. Then, a recent converse theorem is employed, which gives an explicit construction of a Lyapunov function from a finite–step Lyapunov function. This procedure produces additionally an invariant set, through a nonlinear optimization program. An example illustrates the developed procedure and gives insight into the problem complexity",

author = "R.V. Bobiti and M. Lazar",

year = "2014",

doi = "10.1109/ICSTCC.2014.6982397",

language = "English",

pages = "93--98",

booktitle = "Proceedings of the 18th International Conference on System Theory, Control and Computing (ICSTCC) 17-19 October 2014, Sinaia, Romania",

publisher = "Institute of Electrical and Electronics Engineers",

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note = "18th International Conference on System Theory, Control and Computing, ICSTCC 2014, ICSTCC 2014 ; Conference date: 17-10-2014 Through 19-10-2014",

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Bobiti, RV & Lazar, M 2014, On the computation of Lyapunov functions for discrete–time nonlinear systems. in Proceedings of the 18th International Conference on System Theory, Control and Computing (ICSTCC) 17-19 October 2014, Sinaia, Romania. Institute of Electrical and Electronics Engineers, Piscataway, pp. 93-98, 18th International Conference on System Theory, Control and Computing, ICSTCC 2014, Sinaia, Romania, 17/10/14. https://doi.org/10.1109/ICSTCC.2014.6982397

On the computation of Lyapunov functions for discrete–time nonlinear systems. / Bobiti, R.V.; Lazar, M.
Proceedings of the 18th International Conference on System Theory, Control and Computing (ICSTCC) 17-19 October 2014, Sinaia, Romania. Piscataway: Institute of Electrical and Electronics Engineers, 2014. p. 93-98.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

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T1 - On the computation of Lyapunov functions for discrete–time nonlinear systems

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AU - Lazar, M.

N1 - Conference code: 18

PY - 2014

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N2 - This paper considers the problem of computing a Lyapunov function for nonlinear discrete–time systems. The proposed solution is systematic and consists of two steps. First, a pseudo–Lyapunov function, called finite–step Lyapunov function, is computed by solving a finite dimensional nonlinear optimization problem. Then, a recent converse theorem is employed, which gives an explicit construction of a Lyapunov function from a finite–step Lyapunov function. This procedure produces additionally an invariant set, through a nonlinear optimization program. An example illustrates the developed procedure and gives insight into the problem complexity

AB - This paper considers the problem of computing a Lyapunov function for nonlinear discrete–time systems. The proposed solution is systematic and consists of two steps. First, a pseudo–Lyapunov function, called finite–step Lyapunov function, is computed by solving a finite dimensional nonlinear optimization problem. Then, a recent converse theorem is employed, which gives an explicit construction of a Lyapunov function from a finite–step Lyapunov function. This procedure produces additionally an invariant set, through a nonlinear optimization program. An example illustrates the developed procedure and gives insight into the problem complexity

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DO - 10.1109/ICSTCC.2014.6982397

M3 - Conference contribution

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BT - Proceedings of the 18th International Conference on System Theory, Control and Computing (ICSTCC) 17-19 October 2014, Sinaia, Romania

PB - Institute of Electrical and Electronics Engineers

CY - Piscataway

T2 - 18th International Conference on System Theory, Control and Computing, ICSTCC 2014

Y2 - 17 October 2014 through 19 October 2014

ER -

On the computation of Lyapunov functions for discrete–time nonlinear systems

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