Model Approximation of Discrete-Time T-S Fuzzy Time-Delay Systems

Abstract

In this chapter, the $\mathcal{H}_{\infty}$ model approximation problem is studied for discretetime T-S fuzzy time-delay systems. For a given high-order T-S fuzzy system, our attention is focused on the construction of reduced-order models, which approximate the original system well in an $\mathcal{H}_{\infty}$ sense. To reduced the conservativeness caused by the time-delay, the delay partitioning approach is advanced to derive a delay-dependent stability condition with an $\mathcal{H}_{\infty}$ performance for the approximation error system. Based on which, the $\mathcal{H}_{\infty}$ model approximation problem is settled by applying the projection approach, which casts the model approximation into a sequential minimization problem subject to LMI constraints by employing a CCL algorithm. In addition, the $\mathcal{H}_{\infty}$ model approximation problems with special structures, delay-free model and zero-order model, are also obtained.