Abstract
The family of time-dependent rectangular sets, flow invariant with respect to a class of discrete-time nonlinear uncertain systems, is studied. The invariance results are further used for dealing with a special type of asymptotic stability, called componentwise asymptotic stability (CWAS), which can be characterized by difference inequalities. The particularisation of the CWAS conditions for exponential type time-dependence yields the stronger property of componentwise exponential asymptotic stability (CWEAS), that is proven equivalent to some algebraic inequalities.
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Hmamed, A. (1997). “Componentwise stability of 1-D and 2-D linear discrete systems”, Automatica, 33 (9), pp. 1759–1762.
Pastravanu, O. and Voicu, M. (1999). “Flow invariant rectangular sets and componentwise asymptotic stability of interval matrix systems”, Proc. of the 5-th European Control Conference ECC’99, Kalsruhe, CD-ROM.
Pastravanu, O. and Voicu, M. (2001). “Flow invariance in exploring stability of a class of nonlinear uncertain systems”, Proc. of the 6-th European Control Conference ECC’01, Porto, CD-ROM.
Pavel, H. N. (1984). Differential Equations: Flow Invariance and Applications. Research Notes in Mathematics, No. 113, Pitman, Boston.
Voicu, M. (1984a). “Free Response Characterization via flow-invariance”, Prep. of the 9-th World Congress of IFAC, Budapest, Vol. 5, pp. 12–17.
Voicu, M. (1984b). “Componentwise asymptotic stability of linear constant dynamical systems”, IEEE Trans. Automatic Control, 29 (10), pp. 937–939.
Voicu, M. (1987). “On the application of the flow-invariance method in the control theory and design”, Prep. of th 10-th World Congress of IFAC, Munich, Vol. 8, pp. 364–369.
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Marinovici, L., Pastravanu, O. (2003). Flow-Invariance Properties for a Class of Discrete-Time Nonlinear Uncertain Systems. In: Barbu, V., Lasiecka, I., Tiba, D., Varsan, C. (eds) Analysis and Optimization of Differential Systems. SEC 2002. IFIP — The International Federation for Information Processing, vol 121. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-35690-7_27
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DOI: https://doi.org/10.1007/978-0-387-35690-7_27
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