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 2 Some obtained results for our proposed results in this paper

The delay upper bound and stability switching domains for switched system (1a)-(1e) with (10)
[10]	$r_{m} = 1$ , $r_{M} = 5$ (α = 1) (under arbitrary switching signal condition)
[4]	$r_{m} = 1$ , $r_{M} = 6$ (α = 1) (under arbitrary switching signal condition)
[6]	Results fail (switching signal cannot be selected even when no perturbations)
Our result	$r_{m} = 1$ , $r_{M} = 7$ (α = 1, globally asymptotically stable) (σ = 1)
	$r_{m} = 1$ , $r_{M} = 19$ (α = 1, globally asymptotically stable) (σ = 2)
	$r_{m} = 1$ , $r_{M} = 10$ (α = 1) (Choose $α_{1} = 0.1$ and $α_{2} = 0.9$ )
	Switching signal in (3e) with ${\bar{Ω}}_{1} = {{[x_{1} x_{2}]}^{T} \in R^{2} : 5.8081 x_{1}^{2} + 7.1275 x_{1} x_{2} + 1.7783 x_{2}^{2} < 0}$ , ${\bar{Ω}}_{2} = ℜ^{2} ∖ {\bar{Ω}}_{1}$