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The control performance for the problem of interest is quantified by the decline (decay) of the generalized energy of the controlled system. The paper develops (upper and lower) barriers bounding the decay of the system\u2019s generalized energy, which can be achieved over a set of asymptotically stabilizing feedback laws. The corresponding problem is treated without the loss of generality, resulting in a theoretical framework that provides a solid basis for practical implementations. To enhance understanding, the main results are illustrated in a simple example.<\/jats:p>","DOI":"10.2478\/amcs-2019-0046","type":"journal-article","created":{"date-parts":[[2020,1,8]],"date-time":"2020-01-08T09:30:36Z","timestamp":1578475836000},"page":"629-639","source":"Crossref","is-referenced-by-count":0,"title":["Fundamental Limitations of the Decay of Generalized Energy in Controlled (Discrete\u2013Time) Nonlinear Systems Subject to State and Input Constraints"],"prefix":"10.61822","volume":"29","author":[{"given":"Istv\u00e1n","family":"Selek","sequence":"first","affiliation":[{"name":"Systems Engineering Research Group , University of Oulu , Pentti Kaiteran katu 1, 90570 Oulu , Finland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Enso","family":"Ikonen","sequence":"additional","affiliation":[{"name":"Systems Engineering Research Group , University of Oulu , Pentti Kaiteran katu 1, 90570 Oulu , Finland"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"37438","published-online":{"date-parts":[[2019,12,31]]},"reference":[{"key":"2023050313244746835_j_amcs-2019-0046_ref_001_w2aab3b7ab1b6b1ab1ab1Aa","doi-asserted-by":"crossref","unstructured":"Al\u2019brekht, E.G. 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