Checking dissipativity of linear behavior systems given in kernel representation

The behavior approach and the problem of dissipativity have both been introduced and studied extensively by Willems and others. Current methods to check dissipativity will either check the solvability of a linear matrix inequality or rely on symbolic computations with image representations via computer algebra packages. We will discuss a new characterization for linear behavior systems in kernel representation that allows to check dissipativity via the solution of structured eigenvalue problems. The complexity and efficiency of our new method will be compared to the existing methods.