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Research Papers

# Gain-Scheduled $H∞$ Control for Linear Parameter Varying Stochastic Systems

[+] Author and Article Information
Cheung-Chieh Ku

Department of Marine Engineering,
National Taiwan Ocean University,
Keelung 202, Taiwan
e-mail: ccku@mail.ntou.edu.tw

Cheng-I Wu

Department of Marine Engineering,
National Taiwan Ocean University,
Keelung 202, Taiwan
e-mail: hhhhhhhhhh10622@yahoo.com.tw

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received November 24, 2014; final manuscript received July 9, 2015; published online August 20, 2015. Assoc. Editor: Ryozo Nagamune.

J. Dyn. Sys., Meas., Control 137(11), 111012 (Aug 20, 2015) (12 pages) Paper No: DS-14-1497; doi: 10.1115/1.4031059 History: Received November 24, 2014

## Abstract

In this paper, a gain-scheduled controller design method is proposed for linear parameter varying (LPV) stochastic systems subject to $H∞$ performance constraint. Applying the stochastic differential equation, the stochastic behaviors of system are described via multiplicative noise terms. Employing the gain-scheduled design technique, the stabilization problem of LPV stochastic systems is discussed. Besides, the $H∞$ attenuation performance is employed to constrain the effect of external disturbance. Based on the Lyapunov function and Itô's formula, the sufficient conditions are derived to propose the stability criteria for LPV stochastic systems. The derived sufficient conditions are converted into linear matrix inequality (LMI) problems that can be solved by using convex optimization algorithm. Through solving these conditions, the gain-scheduled controller can be obtained to guarantee asymptotical stability and $H∞$ performance of LPV stochastic systems. Finally, numerical examples are provided to demonstrate the applications and effectiveness of the proposed controller design method.

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## Figures

Fig. 1

Responses of example 1 (Theorem 1)

Fig. 2

Responses of example 1 (Theorem 2)

Fig. 3

Responses for x1(t) of example 2

Fig. 4

Responses for x2(t) of example 2

Fig. 5

Responses for x3(t) of example 2

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