Switching law design for finite‐time stability of singular fractional‐order systems with delay

Positivity and stability of mixed fractional‐order systems with unbounded delays: Necessary and sufficient conditions

“…Assume that ≻ 0 satisfying (A + B) ≺ 0. Their approach is to compare solution (⋅, ) of system (15) with the one of the following systems…”

“…In References 13 and 14, by using Lyapunov‐candidate‐functions, the authors proposed some results on stability of fractional systems with delays. An analytical approach based on the Laplace transform and “inf‐sup” method for studying finite‐time stability of singular fractional‐order switched systems with delay was presented in Reference 15. By using the Lyapunov method combined with the concept of uniformly positive definite matrix functions and Hamilton‐Jacobi‐Riccati inequalities, robust stability of the almost periodic solution to uncertain impulsive functional differential systems of fractional order was investigated in Reference 16.…”

A novel finite time stability analysis of nonlinear fractional‐order time delay systems: A fixed point approach

“…Authors in a previous work [25] have presented a robust FTS approach of FOTDSs. On the other hand, dealing with the second group using the Lyapunov functions, the authors in previous study [27] proposed an analytical technique for analyzing the FTS of singular fractional‐order switching systems with delay based on the Laplace transform and the “inf‐sup” technique. Thanh et al in a research [8] have investigated a novel FTS analysis of FOTDSs.…”

“…The demonstration of finite-time bounded stability of fractional-order time delayed systems (FOTDSs) in the literature has been based on different methods and concepts such as the Gronwall inequalities [6,7,[24][25][26] and the Lyapunov functions [8,27]. As for the first group using the Gronwall inequalities, the authors in a previous study [24] have presented a FTS analysis of the FOTDSs using the Caputo-Katugampola derivative.…”

A Novel Finite Time Stability Analysis of Nonlinear Fractional-Order Time Delay Systems: A Fixed Point Approach

“…In a same context, the evolution of engineering and sciences has notably refreshing the use of the FC in numerous areas of the control theory, and this includes FTS [6,18,23,25,31], asymptotic stability [3,20,21,28], stabilization [22], observer design [14,22] and fault estimation [13,15,16]. The demonstration of FTS of FOTDSs in the literature has been based on different methods and concepts such us the Gronwall inequalities [2,6,7,8,18,23,25,32,33] and the Lyapunov functions [29,30,31]. As for the first group using the Gronwall inequalities, the authors in [2] have presented a FTS analysis of the FOTDSs using the Caputo-Katugampola derivative.…”