This chapter introduces some fundamental concepts and definitions used throughout of the book. It shows that all concepts and methodologies developed for TP models in this book can readily be applied in qLPV and LMI based control theories and TS fuzzy model based concepts. This chapter also discusses the HOSVD and the quasi-HOSVD based canonical form of TP functions that will be used as a basic steps in various frameworks proposed in later chapters.
KeywordsTP function TP model TS fuzzy model HOSVD based canonical form
- 3.P. Baranyi, L. Szeidl, P. Várlaki, Y. Yam, Definition of the HOSVD based canonical form of polytopic dynamic models, in Proceedings of the 2006 IEEE International Conference on Mechatronics, Budapest, 3–5 July 2006, pp. 660–665Google Scholar
- 5.L. De Lathauwer, B. De Moor, J. Vandewalle, Dimensionality reduction in higher-order-only ICA, in Proceedings of the IEEE Signal Processing Workshop on Higher-Order Statistics, 1997, Banff, Alberta (1997), pp. 316–320Google Scholar
- 7.M. Ishteva, L. De Lathauwer, P. Absil, S. Van Huffel, Dimensionality reduction for higher-order tensors: algorithms and applications. Int. J. Pure Appl. Math. 42(3), 337 (2008)Google Scholar
- 8.L. Szeidl, P. Várlaki, HOSVD based canonical form for polytopic models of dynamic systems. J. Adv. Comput. Intell. Intell. Inf. 13(1), 52–60 (2009)Google Scholar
- 11.P. Várkonyi, D. Tikk, P. Korondi, P. Baranyi, A new algorithm for RNO-INO type tensor product model representation, in Proceedings of the IEEE 9th International Conference on Intelligent Engineering Systems (2005), pp. 263–266Google Scholar