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 3 The obtained results for our proposed results in this paper

The delay upper bound and stability switching domains for switched system (1a)-(1e) with (11)
[4, 10]	Results fail (under arbitrary switching signal condition)
[6, 7]	Results fail (switching signal cannot be selected even when no perturbations)
Our results	Fail to guarantee the stability of each subsystem in Theorem 2
	$r_{m} = 1$ , $r_{M} = 7$ (α = 1, globally asymptotically stable) ( $α_{1} = α_{2} = 0.5$ )
	Switching signal in (3e) with ${\bar{Ω}}_{1} = {{[x_{1} x_{2}]}^{T} \in ℜ^{2} : 27.9396 x_{1}^{2} + 3.3182 x_{1} x_{2} - 18.2592 x_{2}^{2} < 0}$ , ${\bar{Ω}}_{2} = ℜ^{2} ∖ {\bar{Ω}}_{1}$