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Technical Brief

# Guaranteed Performance State-Feedback Gain-Scheduling Control With Uncertain Scheduling Parameters

[+] Author and Article Information
Ali Khudhair Al-Jiboory

Mechanical Engineering,
Michigan State University,
East Lansing, MI 48824
e-mail: aljiboor@egr.msu.edu

Guoming G. Zhu

Mechanical Engineering,
Michigan State University,
East Lansing, MI 48824
e-mail: zhug@egr.msu.edu

Jongeun Choi

Mechanical Engineering,
Michigan State University,
East Lansing, MI 48824
e-mail: jchoi@egr.msu.edu

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received December 10, 2014; final manuscript received September 20, 2015; published online October 29, 2015. Assoc. Editor: Ryozo Nagamune.

J. Dyn. Sys., Meas., Control 138(1), 014502 (Oct 29, 2015) (7 pages) Paper No: DS-14-1518; doi: 10.1115/1.4031727 History: Received December 10, 2014; Revised September 20, 2015

## Abstract

State-feedback gain-scheduling controller synthesis with guaranteed performance is considered in this brief. Practical assumption has been considered in the sense that scheduling parameters are assumed to be uncertain. The contribution of this paper is the characterization of the control synthesis that parameterized linear matrix inequalities (PLMIs) to synthesize robust gain-scheduling controllers. Additive uncertainty model has been used to model measurement noise of the scheduling parameters. The resulting controllers not only ensure robustness against scheduling parameters uncertainties but also guarantee closed-loop performance in terms of $H2$ and $H∞$ performances as well. Numerical examples and simulations are presented to illustrate the effectiveness of the synthesized controller. Compared to other control design methods from literature, the synthesized controllers achieve less conservative results as measurement noise increases.

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## Figures

Fig. 1

Performance versus ϵ with ζ = 0.2

Fig. 2

Guaranteed performance

Fig. 3

Simulation: (a) measured and exact scheduling parameters and (b) disturbance attenuation responses associated with exact and noisy scheduling parameter

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