Encyclopedia of Systems and Control

Living Edition
| Editors: John Baillieul, Tariq Samad

LMI Approach to Robust Control

  • Kang-Zhi Liu
Living reference work entry
DOI: https://doi.org/10.1007/978-1-4471-5102-9_161-1

Abstract

In the analysis and design of robust control systems, LMI method plays a fundamental role. This article gives a brief introduction to this topic. After the introduction of LMI, it is illustrated how a control design problem is related with matrix inequality. Then, two methods are explained on how to transform a control problem characterized by matrix inequalities to LMIs, which is the core of the LMI approach. Based on these knowledge, the LMI solutions to various kinds of robust control problems are illustrated. Included are \(\mathcal{H}_{\infty }\) and \(\mathcal{H}_{2}\) control, regional pole placement, and gain-scheduled control.

Keywords

LMI Robust control \(\mathcal{H}_{\infty }\) and \(\mathcal{H}_{2}\) control Regional pole placement Gain-scheduled control Multi-objective control 
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Copyright information

© Springer-Verlag London 2013

Authors and Affiliations

  1. 1.Department of Electrical and Electronic EngineeringChiba UniversityChibaJapan