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

Ligang Wu, Xiaojie Su, Peng Shi, Jianbin Qiu
2011 IEEE transactions on fuzzy systems  
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
more » ... ty 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.
doi:10.1109/tfuzz.2011.2104363 fatcat:3rwvrs43u5egfn7rq54yowmney