Local dynamic output feedback control of saturated discrete-time T-S fuzzy systems with partially measured premise variables

Abstract

This paper aims to investigate the problem of designing locally stabilizing dynamic output feedback controllers and estimate the domain of attraction for discrete-time Takagi-Sugeno (T-S) fuzzy systems. A realistic scenario is assumed where the control signal is subject to saturation, and the premise variables are partially or completely unmeasured, that is, not available for the control law. As a result, the fuzzy output controller can have a different number of fuzzy rules and a different set of membership functions from the T-S model. To obtain locally stabilizable conditions, we propose modeling the variation rate of the membership functions without using upper bounds, a new contribution in the context of output control of discrete-time T-S systems. The design conditions are expressed as linear matrix inequality relaxations based on fuzzy Lyapunov functions using slack variables introduced by Finsler's lemma. Numerical examples illustrate the effectiveness of the approach.

Keywords:

• Takagi-Sugeno (T-S) models
• discrete-time
• dynamic output feedback
• linear matrix inequalities (LMIs)
• local stabilization
• input saturation
• domain of attraction
• immeasurable premise variables

Data availability statement

The authors confirm that the data supporting the findings of this study are available within the article (and/or) its supplementary materials.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 The time dependency in ${\mu }_j(z_j)$ is omitted for brevity, and then we adopt the notation ${\mu }_j(z_j+1)$ to denote ${\mu }_j(z_j)$ in the instant k + 1.

2 The equality holds when z is a time-varying parameter independent of the states (Hu & Lin, 2003; Jungers & Castelan, 2011).

Additional information

Funding

This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior – Brasil (CAPES) – Finance Code 001.

Notes on contributors

Eduardo S. Tognetti

Eduardo S. Tognetti is currently an Associate Professor at the Electrical Engineering Department at the University of Brasilia - UnB, Brazil. He received the B.Sc. and M.Sc. degrees in Electrical Engineering from the University of São Paulo - USP, Brazil, in 2002 and 2006, respectively, and the Ph.D. degree in Electrical Engineering from the University of Campinas - UNICAMP, Brazil, in 2011. He worked as an automation engineer with the paper mill Votorantim Pulp and Paper (Fibria S.A.), Brazil, from 2002 to 2011, where he was involved with industrial controllers, process and drive control systems. He held visiting research positions at the University of Kaiserslautern, Germany, in 2014, and at the Research Centre of Automatic Control (CRAN UMR 7039 CNRS, Université de Lorraine) in Nancy, France, from 2018 to 2019. His current research interests include robust and LPV control, T-S fuzzy systems, and network control systems.

Tássio M. Linhares

Tássio M. Linhares received the B.Sc. degree in Mechanical Engineering, the M.Sc. degree in Mechatronic Engineering, and the Ph.D. degree in Electrical Engineering in 2014, 2017, and 2022, respectively, from the University of Brasilia, Brazil. His current research interests include control of dynamical systems and software engineering.