Then following similar procedures to the proof of Theorem 1, the asymptotic stability condition for the T-S system (3.25) is equivalent to sum_{l=1}^{r}h_{l}(t) widetilde{xi}^{mathrm{T}}(t) bigl[widetilde{Xi}_{k}+ operatorname{He}(mathcal{Y}Gamma_{l}) bigr]widetilde{xi}(t)< 0. (3.29) This completes the proof.
for each t ∈ ] 0, T [. In the proof of this lemma we use the procedure similar to the proof of Lemma 3.2.
Using procedures similar to the proof of Theorem 2.1, we can get a more general result as follows.
By using a similar procedure to proof of the [13, Theorem 2.3], we prove that that is continuous on, which completes the proof is completely continuous.
The procedure is relatively similar to the proof of Theorem 3.1, thus we do not include it in this paper.
The proof follows from the Galerkin method; and the compactness method, the procedure is very similar to the proof of Theorem 3.3, and it is even easier.
Similar to the proof procedure of Lemma 2, we only need to show that C ~ is full column rank under condition (22).
Remark 1 Similar to the proof procedure in [11, 15], we can obtain the above relation, thus λ l and p q μ l are called algebraic equivalent, i.e., λ l ∼ p q μ l [14, 15].
Moreover, according to the proof procedure of Lemma 7, we find that, if nδ ( 1 − γ ) ( n R − n T + 1 ) ▵ ζ ≤ n R, the detection outage due to the occurrence of event S n ≥C n might cause diversity order loss to the SCC-ET-FSD for every user; otherwise no loss of diversity order would happen.
We note that the origin is sent to a node and Λ = 2 ( 2 + 3 K ) 8 + 3 K ∉ N, which ensures that the node of system (54) is linearizable, and similar to the proof procedure in Theorem 4.5, one can see that system (53) is also linearizable at the origin.
