Abstract
The various notions of stability usually associated with dynamic systems are cast as uniform continuities. The features of Liapunov functions which typify stability are generalized to a characterization of uniform continuity. General theorems yield necessary and sufficient Liapunov criteria for weak and asymptotic stability and for uniform convergence of series and integrals. For the latter a common generalization of theorems of Weierstrass, Abel and Dirichlet is derived.
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The research reported in this paper was supported in part by National Science Foundation Grant GP-27368.
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Rogers, E.H. Liapunov criteria for uniformity. Math. Systems Theory 9, 232–240 (1975). https://doi.org/10.1007/BF01704021
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DOI: https://doi.org/10.1007/BF01704021