<abstract xmlns="http://www.w3.org/1999/xhtml"><p>This paper is concerned with the problem of designing a robust modiﬁed repetitive-control system with a dynamic output feedback controller for a class of strictly proper plants. Employing the continuous lifting technique, a continuous-discrete two-dimensional (2D) model is built that accurately describes the features of repetitive control. The 2D control input contains the direct sum of the effects of control and learning, which allows us to adjust control and learning preferentially. The singular-value decomposition of the output matrix and Lyapunov stability theory are used to derive an asymptotic stability condition based on a Linear Matrix Inequality (LMI). Two tuning parameters in the LMI manipulate the preferential adjustment of control and learning. A numerical example illustrates the tuning procedure and demonstrates the effectiveness of the method.</p></abstract>

This paper is concerned with the problem of designing a robust modiﬁed repetitive-control system with a dynamic output feedback controller for a class of strictly proper plants. Employing the continuous lifting technique, a continuous-discrete two-dimensional (2D) model is built that accurately describes the features of repetitive control. The 2D control input contains the direct sum of the effects of control and learning, which allows us to adjust control and learning preferentially. The singular-value decomposition of the output matrix and Lyapunov stability theory are used to derive an asymptotic stability condition based on a Linear Matrix Inequality (LMI). Two tuning parameters in the LMI manipulate the preferential adjustment of control and learning. A numerical example illustrates the tuning procedure and demonstrates the effectiveness of the method.

A 2D system approach to the design of a robust modified repetitive-control system with a dynamic output-feedback controller

School of Information and Electrical Engineering Hunan University of Science and Technology, Xiangtan 411201, China

School of Computer Science Tokyo University of Technology, Tokyo 192-0982, Japan

International Journal of Applied Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

This paper is concerned with the problem of designing a robust modiﬁed repetitive-control system with a dynamic output feedback controller for a class of...

A 2D system approach to the design of a robust modified repetitive-control system with a dynamic output-feedback controller

Published Online: Jun 26, 2014

Page range: 325 - 334

Received: Mar 07, 2013

Accepted: Dec 16, 2013

DOI: https://doi.org/10.2478/amcs-2014-0024

Keywords
repetitive control, dynamic output-feedback, two-dimensional system, singular-value decomposition, linear matrix inequality

© 2014 Lan Zhou et al.

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

A 2D system approach to the design of a robust modified repetitive-control system with a dynamic output-feedback controller

Published Online: Jun 26, 2014

Page range: 325 - 334

Received: Mar 07, 2013

Accepted: Dec 16, 2013

DOI: https://doi.org/10.2478/amcs-2014-0024

Keywordsrepetitive control, dynamic output-feedback, two-dimensional system, singular-value decomposition, linear matrix inequality

© 2014 Lan Zhou et al.

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
repetitive control, dynamic output-feedback, two-dimensional system, singular-value decomposition, linear matrix inequality