Abstract
This chapter is devoted essentially to the theory of stability and boundedness of Causal differential equations, using Lyapunov’s method. The concepts of Lyapunov stability have given rise to several notions that are important in applications. For example, other than usual stability concepts originated by Lyapunov, we have partial stability, conditional stability, perfect stability and eventual stability of asymptotically invariant sets, to name a few. Corresponding to these, notions of boundedness have been formulated and sufficient conditions are provided. In order to unify a variety of known concepts of stability and boundedness, it is found beneficial to employ two different measures and obtain criteria in terms of two measures.KeywordsLyapunov FunctionTrivial SolutionStability TheoryDifferential InequalityZero SolutionThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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