In this section, we will study the problem of decentralized SMC for large-scale T-S fuzzy interconnected system.
Consider a continuous-time large-scale fuzzy interconnected system, which consists of
subsystems as below,
(1)Here, we make the following assumptions (Yan, Edwards & Spurgeon 2004):
By using the linear transformation
, the fuzzy system in (1) can be rewritten as the regular form as below,
(3)We further define
(4)Then, it yields
(5)Thus, the decentralized fuzzy SMC problem to be addressed in this paper can be expressed as follows. For the system (1), determine the sliding surface and a reaching motion control law
such that the sliding motion to be specified in (3) is asymptotically stable.