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Stability with respect to part of the variables in systems with impulse effect. (English) Zbl 0588.34044
Effective sufficient conditions are found for stability with respect to part of the variables in systems of ordinary differential equations with impulse effect. The approach presented is based on the specially introduced piecewise continuous Lyapunov functions.

MSC:
34D20 Stability of solutions to ordinary differential equations
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[1] Mil’man, V.D; Myshkis, A.D, On the stability of motion in presence of impulses, Sibirsk. mat. zh., 1, No. 2, 233-237, (1960), [In Russian] · Zbl 1358.34022
[2] Mil’man, V.D; Myshkis, A.D, Random impulses in linear dynamical systems, (), 64-81, [In Russian] · Zbl 0133.10403
[3] Myshkis, A.D; Samoilenko, A.M, Systems with impulses in prescribed moments, Mat. sb. (N.S.), 74, No. 2, (1967), [In Russian] · Zbl 0173.11101
[4] Samoilenko, A.M; Perestjuk, N.A, Stability of the solutions of differential equations with impulse effect, Differentsial’nye uravneniya, 11, 1981-1992, (1977), [In Russian]
[5] Samoilenko, A.M; Perestjuk, N.A, On the stability of systems with impulse effect, Differentsial’nye uravneniya, 11, 1995-2001, (1981), [In Russian]
[6] Gurgula, S.I, Investigation of the stability of the solutions of impulse systems by Ljapunov’s second method, ukrain. mat. zh. no. 1, 100-103, (1982), [In Russian] · Zbl 0508.34038
[7] Rouche, N; Habets, P; Laloy, M, Stability theory by Liapunov’s direct method, (1977), Springer-Verlag New York · Zbl 0364.34022
[8] Oziraner, A.S; Rumjancev, V.V, The method of ljapunov functions in the stability problem for motion with respect to a part of variables, Prikl. mat. mekh., 36, 364-384, (1972), [In Russian]
[9] Yoshizawa, T, Stability theory by Liapunov’s second method, (1966), Math. Soc. of Japan Tokyo · Zbl 0144.10802
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