Feedback control for a class of semi-linear parabolic distributed parameter systems with mixed time delays

Huihui Ji, He Zhang and Baotong Cui

International Journal of Systems Science, 2020, vol. 51, issue 4, 585-600

Abstract: This paper investigates the design problem of collocated feedback controllers for a class of semi-linear distributed parameter systems with mixed time delays. The spatially distributed is divided by a finite number of intermittently local actuators and sensors. In order to deal with the problem of exponential stability analysis, the framework of a class of novel interval Lyapunov functional is established. By utilising Schur complement and linear matrix inequality (LMI) techniques, the corresponding stabilisation condition is then derived. Furthermore, the robust $H_{\infty } $H∞ control problem is considered for the uncertain distributed parameter systems with external load disturbance and mixed time delays. Based on the feedback controller, the $H_{\infty } $H∞ exponentially stability condition is derived for the uncertain systems. Finally, the simulation examples are presented to show the effectiveness of the proposed feedback control approach for Fisher equation and Blake–Scholes option pricing model.

Date: 2020
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DOI: 10.1080/00207721.2020.1737261

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