{"department":[{"_id":"263"}],"type":"conference","citation":{"ama":"Rantzer A, Rüffer BS, Dirr G. Separable Lyapunov functions for monotone systems. In: <i>Proc. 52nd IEEE Conf. Decis. Control</i>. ; 2013:4590–4594.","ieee":"A. Rantzer, B. S. Rüffer, and G. Dirr, “Separable Lyapunov functions for monotone systems,” in <i>Proc. 52nd IEEE Conf. Decis. Control</i>, 2013, pp. 4590–4594.","bibtex":"@inproceedings{Rantzer_Rüffer_Dirr_2013, title={Separable Lyapunov functions for monotone systems}, booktitle={Proc. 52nd IEEE Conf. Decis. Control}, author={Rantzer, Anders and Rüffer, Björn S. and Dirr, Gunther}, year={2013}, pages={4590–4594} }","short":"A. Rantzer, B.S. Rüffer, G. Dirr, in: Proc. 52nd IEEE Conf. Decis. Control, 2013, pp. 4590–4594.","apa":"Rantzer, A., Rüffer, B. S., &#38; Dirr, G. (2013). Separable Lyapunov functions for monotone systems. <i>Proc. 52nd IEEE Conf. Decis. Control</i>, 4590–4594.","chicago":"Rantzer, Anders, Björn S. Rüffer, and Gunther Dirr. “Separable Lyapunov Functions for Monotone Systems.” In <i>Proc. 52nd IEEE Conf. Decis. Control</i>, 4590–4594, 2013.","mla":"Rantzer, Anders, et al. “Separable Lyapunov Functions for Monotone Systems.” <i>Proc. 52nd IEEE Conf. Decis. Control</i>, 2013, pp. 4590–4594."},"user_id":"43497","author":[{"last_name":"Rantzer","full_name":"Rantzer, Anders","first_name":"Anders"},{"first_name":"Björn S.","last_name":"Rüffer","full_name":"Rüffer, Björn S."},{"first_name":"Gunther","last_name":"Dirr","full_name":"Dirr, Gunther"}],"year":"2013","date_created":"2023-01-30T11:51:51Z","status":"public","_id":"40778","abstract":[{"text":"Separable Lyapunov functions play vital roles, for example, in stability analysis of large-scale systems. A Lyapunov function is called max-separable if it can be decomposed into a maximum of functions with one-dimensional arguments. Similarly, it is called sum-separable if it is a sum of such functions. In this paper it is shown that for a monotone system on a compact state space, asymptotic stability implies existence of a max-separable Lyapunov function. We also construct two systems on a non-compact state space, for which a max-separable Lyapunov function does not exist. One of them has a sum-separable Lyapunov function. The other does not.","lang":"eng"}],"publication":"Proc. 52nd IEEE Conf. Decis. Control","title":"Separable Lyapunov functions for monotone systems","date_updated":"2023-01-30T11:59:54Z","page":"4590–4594"}