Next Article in Journal
Cyclotomic Trace Codes
Previous Article in Journal
MapReduce Algorithm for Variants of Skyline Queries: Skyband and Dominating Queries
Article Menu

Export Article

Open AccessArticle

LMI Pole Regions for a Robust Discrete-Time Pole Placement Controller Design

Institute of Automotive Mechatronics, Faculty of Electrical Engineering and Information Technology, Slovak University of Technology in Bratislava, 812 19 Bratislava, Slovakia
Author to whom correspondence should be addressed.
Algorithms 2019, 12(8), 167;
Received: 1 July 2019 / Revised: 2 August 2019 / Accepted: 8 August 2019 / Published: 13 August 2019
PDF [2921 KB, uploaded 13 August 2019]


Herein, robust pole placement controller design for linear uncertain discrete time dynamic systems is addressed. The adopted approach uses the so called “D regions” where the closed loop system poles are determined to lie. The discrete time pole regions corresponding to the prescribed damping of the resulting closed loop system are studied. The key issue is to determine the appropriate convex approximation to the originally non-convex discrete-time system pole region, so that numerically efficient robust controller design algorithms based on Linear Matrix Inequalities (LMI) can be used. Several alternatives for relatively simple inner approximations and their corresponding LMI descriptions are presented. The developed LMI region for the prescribed damping can be arbitrarily combined with other LMI pole limitations (e.g., stability degree). Simple algorithms to calculate the matrices for LMI representation of the proposed convex pole regions are provided in a concise way. The results and their use in a robust controller design are illustrated on a case study of a laboratory magnetic levitation system. View Full-Text
Keywords: robust control; pole placement; LMI regions robust control; pole placement; LMI regions

Figure 1

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

Share & Cite This Article

MDPI and ACS Style

Rosinová, D.; Hypiusová, M. LMI Pole Regions for a Robust Discrete-Time Pole Placement Controller Design. Algorithms 2019, 12, 167.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics



[Return to top]
Algorithms EISSN 1999-4893 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top