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Parameterized LMI Approach to H∞ Control Design for Spatially Invariant Systems

Fatmawati Fatmawati, Roberd Saragih, Riyanto Bambang

Abstract


This paper discusses an approach to the H∞ control design with state feedback for spatially invariant systems. In practice, designing control for that system is difficult since it is of infinite dimension. Hence, we propose a method to design a control system for infinite dimensional systems based on Fourier analysis on the spatial variables, so that the system is reduced to a parameterized family of finite dimensional linear  timeinvariant (LTI) systems. The state feedback H∞ controller is designed via linear matrix inequality (LMI). We derive necessary and sufficient conditions for the existence of the state feedback H∞ controller. In the proposed method, we find that the H∞ controllers are spatially invariant systems. A numerical study of the H∞ control design via LMI to examine the controller performance is presented.

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References


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DOI: http://dx.doi.org/10.21535%2FProICIUS.2007.v3.637

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