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Discrete approximation of impulsive differential inclusions. (English) Zbl 1205.34012

The article deals with the approximation of the solution set and the reachable sets of an impulsive differential inclusion with variable times of impulses. It is related to [T. Donchev, in: Large-scale scientific computing. 6th international conference, LSSC 2007, Sozopol, Bulgaria, June 5–9, 2007. Revised papers. Berlin: Springer. Lecture Notes in Computer Science 4818, 309–316 (2008; Zbl 1229.65111)]. Some test examples illustrate the conditions and the practical estimation of the jump conditions.

MSC:

34A60 Ordinary differential inclusions
34A37 Ordinary differential equations with impulses
93B03 Attainable sets, reachability

Citations:

Zbl 1229.65111
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References:

[1] Aubin J.-P., Impulsive Differential Inclusions and Hybrid Systems: A Viability Approach (2002)
[2] Aubin J.-P., Set-Valued Analysis (1990)
[3] DOI: 10.1109/9.981719 · Zbl 1364.49018 · doi:10.1109/9.981719
[4] Baier R., Differential Equations, Chaos and Variational Problems pp 49– (2007)
[5] DOI: 10.1134/S0005117906030027 · Zbl 1126.93314 · doi:10.1134/S0005117906030027
[6] DOI: 10.1007/s00607-007-0240-4 · Zbl 1151.65060 · doi:10.1007/s00607-007-0240-4
[7] Chahma I., Bayreuth. Math. Schr. 67 pp 3– (2003)
[8] Clarke F., Optimization and Nonsmooth Analysis (1983) · Zbl 0582.49001
[9] DOI: 10.1515/9783110874228 · doi:10.1515/9783110874228
[10] Donchev T., EJDE 66 pp 1– (2006)
[11] Donchev T., Lecture Notes in Comput. Sci 4818 pp 309– (2008)
[12] DOI: 10.1007/BF02241223 · Zbl 0667.65067 · doi:10.1007/BF02241223
[13] DOI: 10.1137/1034050 · Zbl 0757.34018 · doi:10.1137/1034050
[14] Filippova T., WSEAS Trans. Syst. 4 pp 974– (2005)
[15] Girard A., Lecture Notes in Comput. Sci 4981 pp 215– (2008)
[16] DOI: 10.1023/A:1021981217050 · Zbl 1024.34007 · doi:10.1023/A:1021981217050
[17] Kostousova E.K., Discrete Contin. Dyn. Syst. Suppl. 2009 pp 466– (2009)
[18] Lakshmikantham V., Theory of Impulsive Differential Equations (1989) · Zbl 0718.34011 · doi:10.1142/0906
[19] Lempio F., Bayreuth. Math. Schr. 54 pp 149– (1998)
[20] DOI: 10.1137/S0363012993245665 · Zbl 0844.49017 · doi:10.1137/S0363012993245665
[21] Perestyuk N., Impulsive differential Equations with Multivalued and Discontinuous Right-Hand Side (2007) · Zbl 1199.34002
[22] DOI: 10.1023/A:1021895010938 · Zbl 1029.65028 · doi:10.1023/A:1021895010938
[23] Plotnikov V., Differential Equations with Multivalued Right-Hand Side. Asymptotic Methods (1999)
[24] DOI: 10.1142/9789812798664 · doi:10.1142/9789812798664
[25] Van der Schaft A., An Introduction to Hybrid Dynamical Systems 251 (2000) · Zbl 0940.93004 · doi:10.1007/BFb0109998
[26] DOI: 10.1137/040620734 · Zbl 1157.34006 · doi:10.1137/040620734
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