Robust Estimation‐Based Non‐Fragile Control for Discrete‐Time Non‐Linear Systems

• Published in: International journal of robust and nonlinear control Vol. 35; no. 6; pp. 2462 - 2471
• Main Authors: Javanfar, Elham, Rahmani, Mehdi, Kamalul Wafi, Moh
• Format: Journal Article
• Language: English
• Published: Hoboken, USA John Wiley & Sons, Inc 01.04.2025; Wiley Subscription Services, Inc
• Subjects: Control systems; Discrete time systems; Feedback control; Feedback control systems; incremental quadratic inequality; Linear filters; Linear matrix inequalities; Linear systems; non‐fragile control; non‐linear system; robust estimation based‐control; Robustness; sector‐bounded condition; State estimation; State feedback; ℒ∞$$ {\mathcal{L}}_{\infty } $$ stability
• ISSN: 1049-8923; 1099-1239
• DOI: 10.1002/rnc.7806

ABSTRACT In this paper, a novel robust estimation‐based non‐fragile controller is designed for a specific class of discrete‐time, time‐varying, non‐linear systems whose non‐linear term satisfies the incremental quadratic inequality, which is parameterized by a set of multiplier matrices and sector‐bounded conditions. The system is subject to unknown external input with fluctuating controller gain. The proposed approach introduces an improved standard linear filter structure, including non‐linear terms and a modified state feedback controller. The ℒ∞$$ {\mathcal{L}}_{\infty } $$ stability of the closed‐loop system is guaranteed in the framework of linear matrix inequalities (LMIs), and the state estimator and controller gains are determined simultaneously such that the boundedness of the control input is ensured. Moreover, an LMI‐based optimization problem is presented to obtain the closed‐loop system's maximum domain of attraction (DOA). The benchmark system of RTAC is employed to verify the performance of the proposed control approach.