This section will derive the general stability conditions for large-scale T-S fuzzy interconnected systems.
Consider a continuous-time large-scale nonlinear system containing 
subsystems with interconnections, where the 
-th nonlinear subsystem is represented by the following T-S fuzzy model:
Plant Rule 
: IF 
is 
and 
is 
and 
and 
is 
, THEN
(1) where
,
is the number of the subsystems. For the
-th subsystem,
is the
-th fuzzy inference rule;
is the number of inference rules;
are fuzzy sets;
denotes the system state;
are the measurable variables;
is the
-th local model;
denotes the nonlinear interconnection of the
-th and
-th subsystems for the
-th local model.
Define the inferred fuzzy set 
and normalized membership function 
, it yields
(2) where
is the grade of membership of
in
. Here we will denote
for brevity.
By fuzzy blending, the 
-th global T-S fuzzy dynamic model is obtained by
(3) where
(4)Before moving on, we give the following lemma which will be used to derive the main results.
Proof. Note that
(6) which implies that
(7)By taking the relations in (6) and (7), we have
(8)Thus, this proof is completed.