SCIENCE CHINA Information Sciences, Volume 59, Issue 9: 092206(2016) https://doi.org/10.1007/s11432-016-5554-4

## Feedback control for a class of second order hyperbolic distributed parameter systems

• AcceptedSep 30, 2015
• PublishedAug 23, 2016
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### Abstract

This paper deals with the problem of state feedback control for a class of {the} distributed parameter systems with {the} disturbance term. {And} the considered distributed parameter systems are composed of {the} second order hyperbolic partial differential equations. Two different classes of restrictions on the disturbance term are given, one is that the disturbance term satisfies the linear growth constraint condition to the state variables of the system, and the other is that the disturbance term obeys the bound constraint under the significance of $L_2$. Based on {a} variable structure method, the state feedback controllers are obtained by means of constructing appropriate Lyapunov functional. The closed-loop systems are globally asymptotically stable on $W^{1,2}(0,1)\times L_2 (0,1)$ space under the effect of the state feedback control laws. Simulation results illustrate the effectiveness of the proposed method.

### Funded by

National Natural Science Foundation of China(11371013)

### Acknowledgment

Acknowledgments

This work was supported by National Natural Science Foundation of China (Grant No. 11371013).

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