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Robust Stabilization Design for Stochastic Partial Differential Systems Under Spatio-temporal Disturbances and Sensor Measurement Noises

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2 Author(s)
Chen, W.-H. ; Department of Electrical Engineering, Hsiuping University of Science and Technology, Taichung, Taiwan, R.O.C. ; Chen, B.-S.

We investigate an $ {H_{infty} } $ robust observer-based stabilization design problem for linear stochastic partial differential systems (LSPDSs) under spatio-temporal disturbances and sensor measurement noises. A general theoretical $ {H_{infty} } $ robust observer-based stabilization method is introduced at the beginning for LSPDSs under intrinsic fluctuation, external disturbance and sensor measurement noise in the spatio-temporal domain. A complex Hamilton Jacobi integral inequality (HJII) needs to be solved when designing the robust $ {H_{infty} } $ observer-based stabilization for LSPDSs. For simplifying the design procedure, a stochastic state space model is first developed via the semi-discretization finite difference scheme to represent the stochastic partial differential system at each grid node. Then the stochastic state space models at all grid nodes are merged together into a stochastic spatial state space model. Based on this stochastic spatial state space model, an implementable $ {H_{infty} } $ robust stabilization design is proposed for LSPDSs via an iterative linear matrix inequality (ILMI) method. The proposed robust $ {H_{infty} } $ stabilization design can efficiently attenuate the effect of spatio-temporal external disturbances and measurement noises upon LSPDSs from the area energy point of view. Finally, a robust $ {H_{infty} } $ stabilization example simulation is shown to illustrate the design procedure and to confirm the performance of the proposed robust stabilization design method.

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Circuits and Systems I: Regular Papers, IEEE Transactions on  (Volume:60 ,  Issue: 4 )