Parallel and Nonparallel Distributed Compensation Controller Design for T-S Fuzzy Discrete Singular Systems With Distinct Difference Item Matrices

Abstract

The issues of admissibility and controller design for a class of extended T-S fuzzy discrete singular systems (FDSSs) with distinct difference item matrices are discussed in this article. A new augmented system which is the equivalent of the original system is introduced to convert these distinct difference item matrices into the easy treatment form. On this basis, using the fuzzy Lyapunov function (FLF), relaxed sufficient condition is given to ensure the admissibility of unforced systems. This condition is described via strict linear matrix inequalities (LMIs), which facilitates to analyze the admissibility. Meanwhile, the design methods of parallel and nonparallel distributed compensation (PDC and Non-PDC) controllers are also proposed. Finally, the advantages of the developed admissibility and controller design approach are illustrated by three examples.

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“…Nevertheless, in our work, these specifications are considered in the approach designed in the present study. Here, we believe that a numerical comparative study will not provide additional conclusion to the superiority of our scheme regarding the controller defined in [49].…”

“…As discussed in [49], a non-PDC approach cannot be applied to discrete-time fuzzy descriptor systems with model specifications related to unmeasurable premise variables and imperfect membership functions. Nevertheless, in our work, these specifications are considered in the approach designed in the present study.…”