Sufficient conditions for uniform exponential stability andh-stability of some classes of dynamic equations on arbitrary time scales

Reconstruction of nonlinear integral inequalities associated with time scales calculus

“…The conclusion in (2) can be achieved by the arbitrariness of l * , inserting (21) into (16) and (8) simultaneously, integrating the resulting inequality, and taking the benefit of (6) and (7). Explanations are discarded.…”

“…Over the most recent couple of years, great efforts have been made to unify and expand integral inequalities on time scales [5][6][7][8][9][10][11][12]. These essential inequalities are promoted in numerous classifications for the boundedness, uniqueness, and the solutions of various dynamic equations [13][14][15][16].…”

converse theorem for practical $h$-stability of time-varying nonlinear systems

“…Such theorems are usually called converse theorems. In [18,19], Pinto introduced a new notion of stability called h-stability (see [2,3,13]) with the intention of obtaining results about stability for weakly stable dierential systems under some perturbations. The various notions of h-stability include several types of known stability properties as uniform stability, exponential asymptotic stability and uniform Lipschitz stability.…”

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

“…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].…”