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# A Sequential Linear Programming Matrix Method to Insensitive $H∞$ Output Feedback for Linear Discrete-Time Systems

[+] Author and Article Information
Xiang-Gui Guo

Tianjin Key Laboratory for Control Theory & Applications in Complicated System,
School of Electrical Engineering,
Tianjin University of Technology,
Tianjin 300384, China
e-mail: guoxianggui@163.com

Guang-Hong Yang

State Key Laboratory of Synthetical
Automation for Process Industries,
College of Information Science and Engineering, Northeastern University,
Shenyang 110819, China
e-mail: yangguanghong@mail.neu.edu.cn

Contributed by the Dynamic Systems Division of ASME for publication in the Journal of Dynamic Systems, Measurement, and Control. Manuscript received January 20, 2013; final manuscript received September 12, 2013; published online October 15, 2013. Assoc. Editor: Jongeun Choi.

J. Dyn. Sys., Meas., Control 136(1), 014506 (Oct 15, 2013) (7 pages) Paper No: DS-13-1033; doi: 10.1115/1.4025458 History: Received January 20, 2013; Revised September 12, 2013

## Abstract

This paper studies the problem of designing insensitive $H∞$ output-feedback controllers for linear discrete-time systems. The designed controllers are insensitive to additive/multiplicative controller coefficient variations. An LMI-based procedure, which is a sequential linear programming matrix method (SLPMM), is proposed to solve the considered problem which is a nonconvex problem itself. It is worth mentioning that the nonfragile control design method is adopted to obtain an effective solution for accelerating convergence of SLPMM algorithm due to the fact that a good starting point for the iteration is very important.

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