Model Approximation for Discrete-Time State-Delay Systems in the T–S Fuzzy Framework

Authors:
L. Wu;X. Su;P. Shi;J. Qiu
Affiliations:
Space Control and Inertial Technology Research Center, Harbin Institute of Technology, Harbin, China;-;-;-
Venue:
IEEE Transactions on Fuzzy Systems
Year:
2011

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Abstract

This paper is concerned with the problem of ${H}_{infty }$ model approximation for discrete-time Takagi–Sugeno (T–S) fuzzy time-delay systems. For a given stable T– S fuzzy system, our attention is focused on the construction of a reduced-order model, which not only approximates the original system well in an ${H}_{infty }$ performance but is also translated into a linear lower dimensional system. By applying the delay partitioning approach, a delay-dependent sufficient condition is proposed for the asymptotic stability with an ${H}_{infty }$ error performance for the error system. Then, the ${H}_{infty }$ model approximation problem is solved by using the projection approach, which casts the model approximation into a sequential minimization problem subject to linear matrix inequality (LMI) constraints by employing the cone complementary linearization algorithm. Moreover, by further extending the results, ${H}_{infty }$ model approximation with special structures is obtained, i.e., delay-free model and zero-order model. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed methods.