State and first order representations
Jan C. Willems1
Department of Electrical Engineering - SCD (SISTA)
University of Leuven
Kasteelpark Arenberg 10
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.
First, we introduce our notation for the solution sets of linear PDEs in the n real independent variables x = (x1, . . . , xn). Let denote, as usual, the set ...