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Unsolved Problems in Mathematical Systems and Control Theory by Vincent D. Blondel, Alexandre Megretski

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Problem 1.12

State and first order representations

Jan C. Willems1

Department of Electrical Engineering - SCD (SISTA)

University of Leuven

Kasteelpark Arenberg 10

B-3001 Leuven-Heverlee

Belgium

Jan.Willems@esat.kuleuven.ac.be

1 DESCRIPTION OF THE PROBLEM

We conjecture that the solution set of a system of linear constant coefficient PDEs is Markovian if and only if it is the solution set of a system of first order PDEs. An analogous conjecture regarding state systems is also made.

Notation

First, we introduce our notation for the solution sets of linear PDEs in the n real independent variables x = (x1, . . . , xn). Let -179662285 denote, as usual, the set ...

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