In this section, we will study decentralized stabilization for large-scale T-S fuzzy interconnected systems.
Consider a continuous-time large-scale nonlinear interconnected system containing subsystems with interconnections, where the -th nonlinear subsystem is represented by the following T-S fuzzy model:
Plant Rule : IF
THEN
(1) where
,
,
is the number of the subsystems;
is the fuzzy inference rule;
is the number of inference rules;
are fuzzy sets;
and
denotes the system state and control input, respectively;
are the measurable variables;
is the
-th local model;
denotes the nonlinear interconnection of the
-th and
-th subsystems.
Define the inferred fuzzy set and normalized membership function , it yields
(2) where we will denote
for brevity, and
is the grade of membership of
in
.
By fuzzy blending, the -th global T-S fuzzy dynamic model is obtained by
(3) where
(4)A decentralized fuzzy controller is given by:
Plant Rule : IF is and is and and is , THEN
(5) where
is controller gains to be determined.
Similarly, the overall controller can be given by
(6) where
Combined with the fuzzy system in (3) and the fuzzy controller in (6), the closed-loop fuzzy control system can be given by
(7)In this section, our aim is to design a decentralized fuzzy controller (6), such that the closed-loop fuzzy control system is asymptotically stable.