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Stability analysis for time delay control of nonlinear systems in discrete-time domain with a standard discretisation method

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Abstract

This paper provides stability analysis results for discretised time delay control (TDC) as implemented in a sampled data system with the standard form of zero-order hold. We first substantiate stability issues in discrete-time TDC using an example and propose sufficient stability criteria in the sense of Lyapunov. Important parameters significantly affecting the overall system stability are the sampling period, the desired trajectory and the selection of the reference model dynamics.

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Correspondence to Jinoh Lee.

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Jinoh LEE received the B.Sc. degree in Mechanical Engineering from Hanyang University, Seoul, South Korea, in 2003 (awarded Summa Cum Laude), and the M.Sc. and Ph.D. degrees in Mechanical Engineering from the Korea Advanced Institute of Science and Technology, Daejeon, South Korea, in 2012. He is currently a Research Scientist at the Department of Advanced Robotics, Istituto Italiano di Tecnologia (IIT), Genoa, Italy, where he held postdoctoral researcher position from 2012 to 2017. His professional is about robotics and control engineering, which include manipulation of highly redundant robots such as dual-arm and humanoids, robust control of nonlinear systems and compliant robotic system control for safe human-robot interaction.

Gustavo A. MEDRANO-CERDA received the B.Sc. degree in Electro-Mmechanical Engineering from the Universidad Nacional Autonoma de Mexico in 1977, and the M.Sc. and Ph.D. degrees in Control Systems from Imperial College, London, in 1979 and 1982, respectively. From 1982 to 1985 he was an associate professor at the Division de Estudios de Postgrado, Facultad de Ingenieria, Universidad Nacional Autonoma de Mexico. From 1985 to 1986 he was a research fellow at the Department of Engineering, University of Warwick. From 1986 to 2002 he was a lecturer at the Department of Electronic and Electrical Engineering at the University of Salford. During this period he set up the Advanced Control and Robot Locomotion Laboratory at the University of Salford. In 1999 he became a control systems consultant at Las Cumbres Observatory (formerly Telescope Technologies Ltd.) and later in 2002 he joined the company as a senior control engineer pioneering work in H-infinity control system design and implementation for astronomical telescopes. Since 2009 he has been a senior research scientist at the Advanced Robotics Department, Istituto Italiano di Tecnologia. His research interests are in the areas of robust control, adaptive control, modelling and identification, fuzzy systems and advanced robotic applications, in particular to walking robots.

Je Hyung JUNG received his Ph.D. degree in Mechanical Engineering from Korea Advanced Institute of Science and Technology (KAIST), Daejeon, South Korea in 2006. He was a Postdoctoral Fellow in the Biorobotics Institute of Scuola Superiore Sant’Anna, located in Pontedera (Pisa), Italy from 2006 to 2008. Since June 2008, he has been with Tecnalia, where he is currently a senior researcher in Health Division. His research interests include modelling and control of robotic system such as multi degree of freedom manipulators and mobile robots, and design and control of rehabilitation, assistive and wearable (exoskeleton) robots, and variable stiffness materials.

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Lee, J., Medrano-Cerda, G.A. & Jung, J.H. Stability analysis for time delay control of nonlinear systems in discrete-time domain with a standard discretisation method. Control Theory Technol. 18, 92–106 (2020). https://doi.org/10.1007/s11768-020-9125-2

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