Title: New relaxed conditions of continuous delayed Takagi-Sugeno positive systems controlled by state feedback and memory state feedback by LP approach: application to buck converter T-S model

Authors: Rkia Oubah; Ouahiba Benmessaouda; Layla Wakrim

Addresses: LAMIGEP, Moroccan School of Engineering Sciences, Member of Honoris United Universities, Marrakesh, 40000, Morocco ' LAMIGEP, Moroccan School of Engineering Sciences, Member of Honoris United Universities, Marrakesh, 40000, Morocco ' Higher Institute of Maritime studies (ISEM), Casablanca, 20000, Morocco

Abstract: This paper investigates the new relaxed stability conditions in open loop and closed loop of time-varying delay Takagi-Sugeno models while maintaining positivity within closed loop. New delay-dependent conditions of stabilisation in terms of LP approach will be derived by using a Lyapunov-Krasovskii Functional (LKF). The proposed stabilisation conditions are less restrictive than some major published stabilisation conditions. Memoryless state feedback control is also employed in cases when the system in open loop is not positive (for example an electrical system where either a positive or negative input current is possible), that in feedback is necessary to make stable and positive. The benefits of the suggested stabilisation conditions will be demonstrated with a numerical and practical (Buck Converter) examples.

Keywords: LP approach; LKF; Lyapunov-Krasovskii Functional; fuzzy Takagi-Sugeno system; time-varying delay; positive systems; state feedback; memory state feedback; buck converter.

DOI: 10.1504/IJAACS.2026.152275

International Journal of Autonomous and Adaptive Communications Systems, 2026 Vol.19 No.1, pp.122 - 142

Received: 28 Nov 2024
Accepted: 26 May 2025
Published online: 13 Mar 2026 *

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