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

• Published in: IEEE transactions on fuzzy systems Vol. 19; no. 2; pp. 366 - 378
• Main Authors: Wu, Ligang, Su, Xiaojie, Shi, Peng, Qiu, Jianbin
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.04.2011; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Approximation methods; Delay; Delay partitioning; discrete-time systems; Fuzzy systems; Nonlinear systems; Numerical models; Reduced order systems; Studies; Symmetric matrices; Takagi-Sugeno (T-S) fuzzy systems; time delay; {H}_{\infty } model approximation
• ISSN: 1063-6706; 1941-0034
• DOI: 10.1109/TFUZZ.2011.2104363

This paper is concerned with the problem of H ∞ 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 ∞ 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 ∞ error performance for the error system. Then, the H ∞ 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 ∞ 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.