Hankel Norm Model Reduction Of IT2 T-S Fuzzy Systems With Time-Varying Delay

The study of the fuzzy control systems has been topics at the forefront of domestic and foreign in control theory. Complex nonlinear systems are ubiquitous in aviation,aerospace, biotechnology, chemical, electronic networks, power systems and economic fields. It is often difficult to establish a precise mathematical model when using the traditional control methods. Fuzzy control is one of the most important methods of analyzing and solving the problem of nonlinear control system. However, besides the nonlinearity of the systems, obtained T-S fuzzy model usually have high dimensions, which bring difficulties for further analysis and control. To solve these problems, model reduction is proposed in such case. Also, in the practical application of the fuzzy system contains a large number of time-delay systems, so research on fuzzy systems with time delay is significant for many industrial systems with time-delay.This paper is concerned with the problem of Hankel norm model reduction for IT2T-S fuzzy systems with time-varying delay. For a given stable IT2 T-S fuzzy system with time-varying delay, our attention is focused on the construction of a reduced-order system which not only has lower dimension but also approximates the original system with a Hankel norm performance. For continuous and discrete systems, the Hankel norm performance of IT2 T-S fuzzy time-varying delay system is analyzed. When dealing with the discrete case, slack matrices are applied, which involve the membership functions in calculation. Then, based on the analysis of Hankel norm performance, the Hankel norm model reduction problems are solved by using convex linearization. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed methods.Related conclusions are given in the form of linear matrix inequalities(LMIs).