Ultimate boundedness and robust stabilization of bilinear discrete-time systems

N. Athanasopoulos; G. Bitsoris; M. Vassilaki

doi:10.1109/CDC.2011.6161233

Ultimate boundedness and robust stabilization of bilinear discrete-time systems

N. Athanasopoulos
, G. Bitsoris
, M. Vassilaki

Control Systems

Onderzoeksoutput: Hoofdstuk in Boek/Rapport/Congresprocedure › Conferentiebijdrage › Academic › peer review

4 Citaten (Scopus)

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In this paper nonlinear time-varying and bilinear discrete-time systems with additive bounded disturbances are considered. First, conditions guaranteeing uniform ultimate boundedness for time-varying nonlinear systems are established. Then, algebraic conditions ensuring the existence of polyhedral Lyapunov functions, uniform boundedness and positive invariance for closed-loop bilinear systems are obtained. Finally, these results are applied to various robust stabilization problems for bilinear systems subject to persistent additive disturbances. It is shown that these problems can be reduced to a single or a series of linear programming problems.

Originele taal-2	Engels
Titel	Proceedings of the 50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC), 12-15 December 2011, Orlando, Florida, United States
Uitgeverij	Institute of Electrical and Electronics Engineers
Pagina's	4622-4627
DOI's	https://doi.org/10.1109/CDC.2011.6161233
Status	Gepubliceerd - 2011

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10.1109/CDC.2011.6161233

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Athanasopoulos, N., Bitsoris, G., & Vassilaki, M. (2011). Ultimate boundedness and robust stabilization of bilinear discrete-time systems. In Proceedings of the 50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC), 12-15 December 2011, Orlando, Florida, United States (blz. 4622-4627). Institute of Electrical and Electronics Engineers. https://doi.org/10.1109/CDC.2011.6161233

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abstract = "In this paper nonlinear time-varying and bilinear discrete-time systems with additive bounded disturbances are considered. First, conditions guaranteeing uniform ultimate boundedness for time-varying nonlinear systems are established. Then, algebraic conditions ensuring the existence of polyhedral Lyapunov functions, uniform boundedness and positive invariance for closed-loop bilinear systems are obtained. Finally, these results are applied to various robust stabilization problems for bilinear systems subject to persistent additive disturbances. It is shown that these problems can be reduced to a single or a series of linear programming problems.",

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doi = "10.1109/CDC.2011.6161233",

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Athanasopoulos, N, Bitsoris, G & Vassilaki, M 2011, Ultimate boundedness and robust stabilization of bilinear discrete-time systems. in Proceedings of the 50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC), 12-15 December 2011, Orlando, Florida, United States. Institute of Electrical and Electronics Engineers, blz. 4622-4627. https://doi.org/10.1109/CDC.2011.6161233

Ultimate boundedness and robust stabilization of bilinear discrete-time systems. / Athanasopoulos, N.; Bitsoris, G.; Vassilaki, M.
Proceedings of the 50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC), 12-15 December 2011, Orlando, Florida, United States. Institute of Electrical and Electronics Engineers, 2011. blz. 4622-4627.

Onderzoeksoutput: Hoofdstuk in Boek/Rapport/Congresprocedure › Conferentiebijdrage › Academic › peer review

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T1 - Ultimate boundedness and robust stabilization of bilinear discrete-time systems

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AU - Bitsoris, G.

AU - Vassilaki, M.

PY - 2011

Y1 - 2011

N2 - In this paper nonlinear time-varying and bilinear discrete-time systems with additive bounded disturbances are considered. First, conditions guaranteeing uniform ultimate boundedness for time-varying nonlinear systems are established. Then, algebraic conditions ensuring the existence of polyhedral Lyapunov functions, uniform boundedness and positive invariance for closed-loop bilinear systems are obtained. Finally, these results are applied to various robust stabilization problems for bilinear systems subject to persistent additive disturbances. It is shown that these problems can be reduced to a single or a series of linear programming problems.

AB - In this paper nonlinear time-varying and bilinear discrete-time systems with additive bounded disturbances are considered. First, conditions guaranteeing uniform ultimate boundedness for time-varying nonlinear systems are established. Then, algebraic conditions ensuring the existence of polyhedral Lyapunov functions, uniform boundedness and positive invariance for closed-loop bilinear systems are obtained. Finally, these results are applied to various robust stabilization problems for bilinear systems subject to persistent additive disturbances. It is shown that these problems can be reduced to a single or a series of linear programming problems.

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DO - 10.1109/CDC.2011.6161233

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BT - Proceedings of the 50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC), 12-15 December 2011, Orlando, Florida, United States

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Athanasopoulos N, Bitsoris G, Vassilaki M. Ultimate boundedness and robust stabilization of bilinear discrete-time systems. In Proceedings of the 50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC), 12-15 December 2011, Orlando, Florida, United States. Institute of Electrical and Electronics Engineers. 2011. blz. 4622-4627 doi: 10.1109/CDC.2011.6161233

Ultimate boundedness and robust stabilization of bilinear discrete-time systems

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