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Keywords:
stability; boundedness; controllable system of partial differential equations; Ljapunov's function
stability; boundedness; controllable system of partial differential equations; Ljapunov's function
Summary:
In the paper definitions of various kinds of stability and boundedness of solutions of linear controllable systems of partial differential equations are introduced and their interconnections are derived. By means of Ljapunov's functions theorems are proved which give necessary and sufficient conditions for particular kinds of stability and boundedness of the solutions.
References:
[1] H. П. Соколов: О функциях от многомерных матриц и примении их к решению линейных систем дифференциальных уравнений с частными производными. УМЖ, т. 22, No. 6, 1970, 769-782. Zbl 1107.83313
[2] J. Kučera I. Vrkoč: Note on stability of a linear homogeneous control system. Časop. pěst. mat. 95 (1970), 56-61. MR 0277277
[3] F. Tumajer: Ljapunov's method in the theory of the boundedness of linear control flows. (Czech.) Časop. pěst. mat. 98 (1973), 278-284. MR 0326094
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