University of Oulu

Selek, I., & Ikonen, E. (2019). Fundamental Limitations of the Decay of Generalized Energy in Controlled (Discrete–Time) Nonlinear Systems Subject to State and Input Constraints. International Journal of Applied Mathematics and Computer Science, 29(4), 629–639.

Fundamental limitations of the decay of generalized energy in controlled (discrete–time) nonlinear systems subject to state and input constraints

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Author: Selek, István1; Ikonen, Enso1
Organizations: 1Systems Engineering Research Group University of Oulu, Pentti Kaiteran katu 1, 90570 Oulu, Finland
Format: article
Version: published version
Access: open
Online Access: PDF Full Text (PDF, 0.5 MB)
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Language: English
Published: De Gruyter, 2019
Publish Date: 2020-02-28


This paper is devoted to the analysis of fundamental limitations regarding closed-loop control performance of discrete-time nonlinear systems subject to hard constraints (which are nonlinear in state and manipulated input variables). 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’s 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.

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Series: International journal of applied mathematics and computer science
ISSN: 1641-876X
ISSN-E: 2083-8492
ISSN-L: 1641-876X
Volume: 29
Issue: 4
Pages: 629 - 639
DOI: 10.2478/amcs-2019-0046
Type of Publication: A1 Journal article – refereed
Field of Science: 213 Electronic, automation and communications engineering, electronics
111 Mathematics
Copyright information: © 2019 I. Selek and E. Ikonen This is an open access article distributed under the Creative Commons Attribution-NonCommercial-NoDerivs license (