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

Abstract

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,

978-1-5225-2385-7.ch006.m02
(1)

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

  • 1.

    978-1-5225-2385-7.ch006.m03;

  • 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

    978-1-5225-2385-7.ch006.m06
    (2)

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,

978-1-5225-2385-7.ch006.m08
(3)

We further define

978-1-5225-2385-7.ch006.m09
(4)

Then, it yields

978-1-5225-2385-7.ch006.m10
(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 978-1-5225-2385-7.ch006.m11 such that the sliding motion to be specified in (3) is asymptotically stable.

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