In this paper the concept of the stability of general functional systems given by M. D. Mesarovic and Y. Takahara is generalized, and the concepts of stability and uniform stability of the generalized model of systems introduced by Yonghao Ma and Yi Lin are given. The relations between the concepts posed by M. D. Mesarovic and Y. Takahara and ours and between the stability and the continuity of functions are studied. In the last section, the preimages of stable systems and uniformly stable systems under homomorphic mappings and system-continuous mappings are studied. Some open questions are posed.
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Lin et al. (1987) studied this question.
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