93-02 Research exposition (monographs, survey articles)
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The behavior approach and the problem of dissipativity have both been introduced and studied extensively by Willems et al. However, a computationally feasible method to check dissipativity is missing. Current methods will mostly rely on symbolic representations of rational functions. We will discuss a new characterization for linear systems in behavior form that allows to check dissipativity via the solution of a para-Hermitian, polynomial eigenvalue problem. Thus, we can employ standard methods of cubic complexity.