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Theory and Modern Applications

Table 1 The obtained results for our proposed results in this paper

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

The delay upper bound and stability switching domains for switched system (1a)-(1e) with (9)

[6]

r m =1, r M =2 (α = 1, globally asymptotically stable)

Ω ¯ 1 ={ [ x 1 x 2 ] T ∈ R 2 :−12.0213 x 1 2 −38.8254 x 1 x 2 −31.6356 x 2 2 <0}, Ω ¯ 2 = ℜ 2 ∖ Ω ¯ 1

Our results

r m =1, r M =178 (α = 1, globally asymptotically stable) (σ = 1)

r m =1, r M =392 (α = 1, globally asymptotically stable) (σ = 2)

r m =1, r M =186 (α = 1, globally asymptotically stable) ( α 1 = α 2 =0.5)

Ω ¯ 1 ={ [ x 1 x 2 ] T ∈ R 2 :0.2018 x 1 2 +0.3982 x 1 x 2 −0.2247 x 2 2 <0}, Ω ¯ 2 = ℜ 2 ∖ Ω ¯ 1

r m =1, r M =20 (α = 0.95, globally exponentially stable) ( α 1 = α 2 =0.5)

Ω ¯ 1 ={ [ x 1 x 2 ] T ∈ R 2 :0.6762 x 1 2 +1.8317 x 1 x 2 +0.2681 x 2 2 <0}, Ω ¯ 2 = ℜ 2 ∖ Ω ¯ 1