Practical stability, boundedness criteria and Lagrange stability of fuzzy differential systems

Stability of Perturbed Set Differential Equations Involving Causal Operators in Regard to Their Unperturbed Ones considering Difference in Initial Conditions

“…Note that UðtÞ and also UðtÞ, VðtÞ, and WðtÞ are solutions of ( 10) and ( 11), (12), and ( 13) if and only if they satisfy (16) on J 1 and ( 17), (18), and (19) on J 2 , respectively. Furthermore, to resemble the behavioral properties of solution of (10) with these of solution of an ordinary correspondent one, we assume that U 0 = Z 0 + U * 0 to ensure the existence of the Hukuhara difference U * 0 = U 0 − Z 0 .…”

“…On other hand, stability analysis [12,[14][15][16][17][18][19][20][21] can be useful for determining the qualitative properties, which in its turn leads to a more perceptive behavioral look of the differential equation's solutions, even when they are unknown explicitly [5,6].…”

Practical stability of time‐varying positive systems with time delay

“…Practical stability which was introduced by LaSalle and Lefschetz first in 1961 in [17] can deal with this situation well. In [18,19,21], corresponding criteria are provided for several non-linear systems by the practical stability of comparison system. Generally speaking, a proper comparison system is proposed firstly and this comparison system is practically stable.…”

Practical stability analysis of perturbed fuzzy control system related to unperturbed fuzzy control system

“…In some status, a system in theory may be stable or asymptotically stable, but it is unstable in practice essentially because the stable domain or the domain of attraction is not large enough to authorize the desired deflection to cancel out [26]. Conversely, occasionally the desired state of a system may be mathematically unstable and nevertheless the system may pendulate enough near this state in which its performance is admissible.…”

“…It is studied about the stability of the fuzzy control differential equation in paper [5,10,20], about practical stability of the fuzzy differential equation in paper [8,26,28], about stability of perturbed system related to unperturbed system in paper [25,27]. In the light of all these studies, Lyapunov's second method is applied on perturbed fuzzy control system related to unperturbed fuzzy control system and its practical stability was studied along with other stability features in this paper.…”