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Regional Stability of Nonlinear Sampled-Data Controlled Systems Under Actuator Saturation: A Quasi-LPV Approach

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Accounting for Constraints in Delay Systems

Part of the book series: Advances in Delays and Dynamics ((ADVSDD,volume 12))

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Abstract

This chapter addresses the stability analysis of sampled-data control for a class of continuous-time nonlinear systems. The proposed approach is based on a local quasi-LPV (Linear Parameter Varying) model for the nonlinear system and the use of a parameter dependent looped-functional to deal with the aperiodic sampling effects. Moreover, the bounds on the control inputs imposed by the physical actuators are also explicitly considered. The effects of the control saturation on the stability are tackled through a parameter dependent generalized sector condition. From these ingredients, conditions in an LMI form are proposed to assess local stability. These conditions are then incorporated in convex optimization problems aiming at obtaining maximized estimates of the region of attraction of the origin or maximizing the inter-sampling time for which the stability is ensured regionally.

The authors are also supported by Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPQ), under grants 306223/2018-0 and 307449/2019-0, and Coordenacão de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)—Finance Code 001, Brazil.

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Author information

Authors and Affiliations

  1. School of Engineering, Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, Brazil

    Alessandra Helena Kimura Palmeira, Joao Manoel Gomes da Silva Jr. & Jeferson Vieira Flores

Authors
  1. Alessandra Helena Kimura Palmeira
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  2. Joao Manoel Gomes da Silva Jr.
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  3. Jeferson Vieira Flores
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Corresponding author

Correspondence to Joao Manoel Gomes da Silva Jr. .

Editor information

Editors and Affiliations

  1. Laboratoire des Signaux et Systèmes, CentraleSupélec, Gif-sur-Yvette, France

    Giorgio Valmorbida

  2. Department of Computer Science, KU Leuven, Heverlee, Belgium

    Wim Michiels

  3. Department of Information Engineering, Computer Science, and Mathematics, University of L’Aquila, L'Aquila, Italy

    Pierdomenico Pepe

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Palmeira, A.H.K., Gomes da Silva, J.M., Flores, J.V. (2022). Regional Stability of Nonlinear Sampled-Data Controlled Systems Under Actuator Saturation: A Quasi-LPV Approach. In: Valmorbida, G., Michiels, W., Pepe, P. (eds) Accounting for Constraints in Delay Systems. Advances in Delays and Dynamics, vol 12. Springer, Cham. https://doi.org/10.1007/978-3-030-89014-8_10

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