Geodesic
Stability and boundedness of controllable continuous flows
Applications of Mathematics, Tome 33 (1988) no. 6, pp. 493-504
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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.
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.
DOI : 10.21136/AM.1988.104327
Classification : 34D20, 34D99, 34H05, 47H20, 58F25, 93C15, 93D05
Keywords: 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 
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Tumajer, František. Stability and boundedness of controllable continuous flows. Applications of Mathematics, Tome 33 (1988) no. 6, pp. 493-504. doi: 10.21136/AM.1988.104327

[1] J. Dieudonné: Foundations of modem analysis. Academic Press, New York-London 1960. Russian translation: Mir, Moscow, 1964. | MR

[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 | Zbl

[3] F. Tumajer: Ljapunov's method in the theory of boundedness of linear controlled flows. (Czech.) Časopis pěst. mat. 98 (1973), 278-284. | MR

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