On the practical stability with respect toh-manifolds of hybrid Kolmogorov systems with variable impulsive perturbations

Impulsive Control Via Variable Impulsive Perturbations on a Generalized Robust Stability for Cohen–Grossberg Neural Networks With Mixed Delays

“…is defined for t ≥ 0 for any values of the uncertain parameters. We will adopt the notion of stability of solutions with respect to h−manifolds [28]- [34] to the equilibrium state of the Cohen-Grossberg model u * of (4) as follows: Definition 1. The equilibrium state u * of (4) is said to be globally exponentially stable with respect to the function h, if for any initial function ϕ 0 ∈ PC, we have…”

“…Among the proved applications of stability with respect to manifolds notion are observer designs [25], celestial mechanics [26], maneuvering systems [27]. Because of the great possibilities for applications, the topic of h−stability whether or not related to equilibrium states has been studied for different types of systems [28]- [30], including some very recent results [31]- [34].…”