Abstract
In this paper, we present a new notion of stability for nonlinear systems of differential equations called practical h-stability. Necessary and sufficient conditions for practical h-stability are given using the Lyapunov theory. Our original results generalize well-known fundamental results: practical exponential stability, practical asymptotic stability, and practical stability for nonlinear time-varying systems. In addition, these results are used to study the practical h-stability of two important classes of nonlinear systems, namely perturbed and cascaded systems. The last part is devoted to the study of the problem of practical h-stabilization for certain classes of nonlinear systems.
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