Sliding-Mode Control of Large-Scale Fuzzy Interconnected Systems

Sliding-Mode Control of Large-Scale Fuzzy Interconnected Systems

DOI: 10.4018/978-1-5225-2385-7.ch006


This chapter will study the decentralized SMC for large-scale fuzzy interconnected systems. The design result on the decentralized sliding mode control of the continuous-time systems is derived in terms of LMIs. We also extend the result to discrete-time systems. Two simulation examples are provided to validate the advantage of the proposed methods.
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6.2 Decentralized Sliding-Mode Control

In this section, we will study the problem of decentralized SMC for large-scale T-S fuzzy interconnected system.

6.2.1 Problem Formulation

Consider a continuous-time large-scale fuzzy interconnected system, which consists of 978-1-5225-2385-7.ch006.m01 subsystems as below,


Here, we make the following assumptions (Yan, Edwards & Spurgeon 2004):

  • 1.


  • 2.

    All the pairs 978-1-5225-2385-7.ch006.m04 are completely controllable;

  • 3.

    There exists a matrix 978-1-5225-2385-7.ch006.m05 such that


By using the linear transformation 978-1-5225-2385-7.ch006.m07, the fuzzy system in (1) can be rewritten as the regular form as below,


We further define


Then, it yields


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 978-1-5225-2385-7.ch006.m11 such that the sliding motion to be specified in (3) is asymptotically stable.

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