Title: H_∞ stabilisation of uncertain discrete time-delayed system with actuator saturation by using Wirtinger inequality

Authors: Komal Agrawal; Richa Negi; Vipin Chandra Pal; Vishwajeet Patel

Addresses: Department of Electrical Engineering, Motilal Nehru National Institute of Technology, Prayagraj, Uttar Pradesh, 211002, India ' Department of Electrical Engineering, Motilal Nehru National Institute of Technology, Prayagraj, Uttar Pradesh, 211002, India ' Department of Electronics and Instrumentation Engineering, National Institute of Technology Silchar, Assam, 788010, India ' Department of Electrical Engineering, Motilal Nehru National Institute of Technology, Prayagraj, Uttar Pradesh, 211002, India

Abstract: This paper contemplates the H_∞ control of discrete-time delayed systems together with actuator saturation, parametric uncertainties and disturbances. H_∞-based state feedback controller is conceived to stabilise the closed loop system. Lyapunov Krasovskii functional (LKF), discrete Wirtinger-based summation inequality and convex hull approach are combined to obtain novel regional stability conditions. The estimated attraction domain is maximised using an optimisation method along with linear matrix inequality (LMI). A comparative study is shown between the obtained and existing findings. The results are found to be less conservative than the prior ones. Finally, instances signify efficacy of presented approaches.

Keywords: time-delay; discrete system; actuator saturation; linear matrix inequality; LMI; H_∞ control; Wirtinger inequality.

DOI: 10.1504/IJAAC.2023.127299

International Journal of Automation and Control, 2023 Vol.17 No.1, pp.43 - 72

Received: 30 May 2021
Accepted: 07 Aug 2021
Published online: 30 Nov 2022 *