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Distributed control of spatially invariant systems using fast iterative solutions to rationally parametric matrix problems

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2 Author(s)
Justin K. Rice ; Delft Center for Systems and Control, Delft University, 2628CD, The Netherlands ; Michel Verhaegen

We consider the problem of analysis and control of spatially invariant discretely distributed systems. It is well known that for certain types of subsystem models, the interconnected systems can be represented by infinite dimensional Laurent operators with rational symbols. Using Fourier techniques, the resulting analysis and control problems can be written as finite dimensional eigenvalue inequalities, Lyapunov equations, and Riccati equations rationally parametric over the unit circle. However, exploiting this paradigm for efficient analysis and synthesis computations has hitherto been difficult. In this paper, we develop computationally efficient iterative methods for finding rational approximations to the solutions of such problems to arbitrary accuracy.

Published in:

Decision and Control, 2009 held jointly with the 2009 28th Chinese Control Conference. CDC/CCC 2009. Proceedings of the 48th IEEE Conference on

Date of Conference:

15-18 Dec. 2009