The system is nonlinear described by a set of 8 ODEs (8 states). Two discontinuous functions (jump discontinuity) are present in the first state equation. Can any one suggest the method to design a TS fuzzy model for such system?

dx1/dt = -x1.x3 + k12.x2 + EGP(1 - x5) - F - Fr + u1

dx2/dt = x1.x3 - k12.x2 - x2.x4

dx3/dt = -ka1.x3 + kb1.x6

dx4/dt = -ka1.x4 + kb1.x6

dx5/dt = -ka1.x5 + kb1.x6

dx6/dt = -ke.x6 + ki.x7

dx7/dt = -ki.x7 + ki.x8

dx8/dt = -ki.x8 + u2

states: [x1 x2 x3 x4 x5 x6 x7 x8]

parameters: [k12 EGP ka1 ka2 ka3 kb1 kb2 kb3 ki ke]

dis-continuous functions: [1] Fr = 0.003(x1-9), when x1>=9

                                              Fr = 0, [otherwise]

                                         [2] F = 0.97 , when x1>=4.5

                                              F = 0.97.x1/4.5  [otherwise]

Q/ How to take the discontinuous functions as premise variables of fuzzy model?