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uniform stability of a set with respect to a flow; uniform boundedness of a flow with respect to a set; controllable continuous flow; controllable system of differential equations
In the paper the concept of a controllable continuous flow in a metric space is introduced as a generalization of a controllable system of differential equations in a Banach space, and various kinds of stability and of boundedness of this flow are defined. Theorems stating necessary and sufficient conditions for particular kinds of stability and boundedness are formulated in terms of Ljapunov functions.
[1] J. Dieudonné: Foundations of modem analysis. Academic Press, New York-London 1960. Russian translation: Mir, Moscow, 1964. MR 0120319
[2] F. Tumajer: Uniform stability and uniform asymptotic stability of sets with respect to a continuous flow. (Czech.) Časopis pěst. mat. 97 (1972), 86-93. MR 0306650 | Zbl 0235.34103
[3] F. Tumajer: Ljapunov's method in the theory of boundedness of linear controlled flows. (Czech.) Časopis pěst. mat. 98 (1973), 278-284. MR 0326094
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