Sufficient conditions for global exponential stability of discrete switched time-delay systems with linear fractional perturbations via switching signal design

Advances in Continuous and Discrete Models

Theory and Modern Applications

Table 4 The obtained results for our proposed results in this paper

The delay upper bound and stability switching domains for switched system (1a)-(1e) with (13)
[4, 10]	Results fail (under arbitrary switching signal condition)
[7]	$r_{m} = 1$ , $r_{M} = 4$ (α = 1, globally asymptotically stable)
[7]	${\bar{Ω}}_{1} = {{[x_{1} x_{2}]}^{T} \in R^{2} : - 0.9918 x_{1}^{2} - 0.035 x_{1} x_{2} - 1.4672 x_{2}^{2} < 0}$ , ${\bar{Ω}}_{2} = ℜ^{2} ∖ {\bar{Ω}}_{1}$
Our results	$r_{m} = 1$ , $r_{M} = 7$ (α = 1, globally asymptotically stable) σ = 1 (Theorem 2)