Paper MoP13.4
Quadrat, Alban (INRIA Sophia Antipolis, France), Robertz, Daniel (RWTH Aachen, Germany)
Constructive Computation of Flat Outputs of a Class of Multidimensional Linear Systems with Variable Coefficients
Scheduled for presentation during the Mini-Symposium "Symbolic Methods in Multidimensional Systems Theory" (MoP13), Monday, July 24, 2006,
16:35−17:00, Room 101
17th International Symposium on Mathematical Theory of Networks and Systems, July 24-28, 2006, Kyoto, Japan
This information is tentative and subject to change. Compiled on March 28, 2024
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Keywords Multidimensional systems, Algebraic systems theory, Behavioral approach to systems theory
Abstract
The purpose of this paper is to give a constructive algorithm for the computation of bases of finitely presented free modules over the Weyl algebras of differential operators with polynomial or rational coefficients. In particular, we show how to use these results in order to recognize when a multidimensional linear system defined by partial differential equations with polynomial or rational coefficients is flat and, if so, to compute flat outputs and the injective image representations of the system. These new results are based on recent constructive proofs of a famous result in non-commutative algebra due to J. T. Stafford. The different algorithms have been implemented in the package Stafford based on OreModules. These results allow us to achieve the general solution of the so-called Monge problem for multidimensional linear systems defined by partial differential equations with polynomial or rational coefficients. Finally, we constructively answer an open question posed by Datta on the possibility to generalize the results of F. Malrait, P. Martin, P. Rouchon, Dynamic feedback transformations of controllable linear time-varying systems, in Lecture Notes in Control and Inform. Sci. 259, Springer, 2001, pp. 55-62, to multi-input multi-output polynomial time-varying controllable linear systems. We show that every controllable ordinary differential linear system with at least two inputs and polynomial coefficients is flat.
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