Title: Robust PD controller design for uncertain system with time-varying delay via singular system approach

Authors: Linlin Zhang; Dan Liu; Li-wei Li; Yefeng Liu; Mouquan Shen

Addresses: College of Electrical Engineering and Control Science, Nanjing Tech University, Nanjing, 211816, China ' College of Electrical Engineering and Control Science, Nanjing Tech University, Nanjing, 211816, China ' College of Electrical Engineering and Control Science, Nanjing Tech University, Nanjing, 211816, China ' Liaoning Key Laboratory of Information Physics Fusion and Intelligent Manufacturing for CNC Machine, Shenyang Institute of Technology, Fushun, 113122, Liaoning, China ' College of Electrical Engineering and Control Science, Nanjing Tech University, Nanjing, 211816, China

Abstract: This paper is dedicated to proportional derivative control of a class of systems subject to parameter uncertainties and time-varying delay. With the help of relaxed state transformation, the resultant closed-loop system with PD controller is presented in terms of singular approach. Setting up an approximate Lyapunov-Krasovskii functional, sufficient conditions are established to ensure the asymptotic stability of the closed-loop system by resorting Bessel-Legendre inequality method to deal with time-varying delay. A structure separation technique is utilised to decouple the interconnection among the introduced transformation matrix, PD controller gains, Lyapunov variable so that they could be solved by means of linear matrix inequality (LMI) technology. The effectiveness of the proposed schemes is verified by numerical examples.

Keywords: robust PD controller; Bessel-Legendre inequality; time-varying delay.

DOI: 10.1504/IJANS.2022.130499

International Journal of Applied Nonlinear Science, 2022 Vol.3 No.4, pp.337 - 357

Received: 30 Mar 2022
Accepted: 20 May 2022
Published online: 24 Apr 2023 *

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