Robust ℋ_∞ and ℒ_∞–ℒ_∞ sampled-data dynamic output-feedback control for nonlinear system in T–S form including singular perturbation

ABSTRACT

This paper pays attention to the robust sampled-data dynamic output-feedback stabilisation problems for a singularly perturbed nonlinear system in Takagi–Sugeno (T–S) form when the system suffers from parametric uncertainties and ${\mathcal{L}}_2$ or ${\mathcal{L}}_{\mathrm{\infty }}$ disturbances. Two design conditions are proposed in terms of linear matrix inequalities such that the admissible controllers guarantee the prescribed ${\mathcal{H}}_{\mathrm{\infty }}$ and ${\mathcal{L}}_{\mathrm{\infty }}$–${\mathcal{L}}_{\mathrm{\infty }}$ disturbance-attenuation levels, respectively. The features of the development are that (i) the sampled-data syntheses are performed in a continuous-time domain and (ii) (even approximate) discrete-time modelling of the T–S fuzzy system is not involved.

Keywords:

• Takagi–Sugeno (T–S) fuzzy system
• singular perturbation
• ${\mathcal{H}}_{\mathrm{\infty }}/{\mathcal{L}}_{\mathrm{\infty }}$–${\mathcal{L}}_{\mathrm{\infty }}$ sampled-data control
• dynamic output feedback

Disclosure statement

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

Correction Statement

This article has been republished with minor changes. These changes do not impact the academic content of the article.

Additional information

Funding

This research was supported by the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2017R1D1A1B03034587) and the Ministry of Science and ICT the Korea government (NRF-2020R1F1A1075776).

Notes on contributors

Jaejun Lee

Jaejun Lee received his B.S. and M.S degrees from the Department of Electronic Engineering, Inha University, Incheon, Korea, in 2018 and 2020, respectively. Since 2020, he has been a Research Engineer with LIG Nex1. His research interests include robust control, sampled-data control, and fuzzy systems.

Ji Hyun Moon

Ji Hyun Moon received his B.S., M.S., and Ph.D. degrees from the Department of Electronic Engineering, Inha University, Incheon, Korea, in 2012, 2014, and 2019, respectively. Since 2019, he has been with the Institute of Technology, Doosan Infracore, Incheon, Korea, where he is currently a Research Engineer. His research interests include fuzzy control systems, multi-agent systems, underwater gliders, excavators, and their applications.

Ho Jae Lee

Ho Jae Lee received his B.S., M.S., and Ph. D. degrees from the Department of Electrical and Electronic Engineering, Yonsei University, Seoul, Korea, in 1998, 2000, and 2004, respectively. In 2005, he was a Visiting Assistant Professor with the Department of Electrical and Computer Engineering, University of Houston, Houston, TX. Since 2006, he has been with the Department of Electronic Engineering, Inha University, Incheon, Korea, where he is currently a Professor. His research interests include fuzzy control systems, sampled-data control, large-scale systems, multi-agent systems, and underwater gliders.