## Abstract and Applied Analysis

### Robust ${H}_{\infty }$ Control for a Class of Nonlinear Distributed Parameter Systems via Proportional-Spatial Derivative Control Approach

#### Abstract

This paper addresses the problem of robust ${H}_{\infty }$ control design via the proportional-spatial derivative (P-sD) control approach for a class of nonlinear distributed parameter systems modeled by semilinear parabolic partial differential equations (PDEs). By using the Lyapunov direct method and the technique of integration by parts, a simple linear matrix inequality (LMI) based design method of the robust ${H}_{\infty }$ P-sD controller is developed such that the closed-loop PDE system is exponentially stable with a given decay rate and a prescribed ${H}_{\infty }$ performance of disturbance attenuation. Moreover, a suboptimal ${H}_{\infty }$ controller is proposed to minimize the attenuation level for a given decay rate. The proposed method is successfully employed to address the control problem of the FitzHugh-Nagumo (FHN) equation, and the achieved simulation results show its effectiveness.

#### Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2013), Article ID 631071, 8 pages.

Dates
First available in Project Euclid: 26 March 2014

https://projecteuclid.org/euclid.aaa/1395858112

Digital Object Identifier
doi:10.1155/2014/631071

Mathematical Reviews number (MathSciNet)
MR3166634

Zentralblatt MATH identifier
07022777

#### Citation

Yang, Cheng-Dong; Qiu, Jianlong; Wang, Jun-Wei. Robust ${H}_{\infty }$ Control for a Class of Nonlinear Distributed Parameter Systems via Proportional-Spatial Derivative Control Approach. Abstr. Appl. Anal. 2014, Special Issue (2013), Article ID 631071, 8 pages. doi:10.1155/2014/631071. https://projecteuclid.org/euclid.aaa/1395858112

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