Convex synthesis of localized controllers for spatially invariant systems

Authors:
Gustavo Ayres De Castro;Fernando Paganini
Affiliations:
Electrical Engineering Department, 66-147F Engineering IV Building, University of California (UCLA), Los Angeles Box 951594, Los Angeles, CA 90095-1594, USA;Electrical Engineering Department, 66-147F Engineering IV Building, University of California (UCLA), Los Angeles Box 951594, Los Angeles, CA 90095-1594, USA
Venue:
Automatica (Journal of IFAC)
Year:
2002

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Abstract

A method is presented to impose localization in controller design for distributed arrays with underlying spatial invariance. The method applies to either state or output feedback problems where the performance objective (e.g., stabilization, H"2 or H"~ control) can be stated in terms of the search for a suitable Lyapunov matrix over spatial frequency. By restricting this matrix to be constant across frequency, controller localization can be naturally imposed. Thus, we obtain sufficient conditions for the existence of a controller with the desired localization and performance, which take the form of linear matrix inequalities (LMIs) over spatial frequency. For one-dimensional arrays, we further show how to convert these conditions exactly to finite-dimensional LMIs by means of the Kalman-Yakubovich-Popov Lemma; extensions to the multi-dimensional case are also discussed.