I was looking for bounds on the controllability gramian matrix in integral form. Are there any known norms to compare different gramians?
please see
Conference Paper Empirical observability Gramian rank condition for weak obse...
https://www.imus.us.es/DOC-COURSE10/PDF/TransparenciasDocCourseTema3.pdf
https://pdfs.semanticscholar.org/f8df/840cb52ff6ba32717ba0bca27eebec0b21a5.pdf
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