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Subscripts 0,1,2 used with the aforementioned parameters refer to the cart, first (bottom) pendulum and second (top) pendulum correspondingly.

Parameter value m0=1,5 kg, m1=0,5 kg, m2= 0,75 kg, L1= 0,5 m, L2= 0,75 m.

Where θ1 and θ2 denotes the angle(in radians) of the pendulum from the vertical, dθ1/dt and dθ2/dt are angular velocities. G=9,8 m/s2 is the gravity constant. m0 is mass of the cart, m1 is mass of the first pendulum link, m2 is mass of the second pendulum link. L1 is length of

the first pendulum link, L2 is the second pendulum link. You will solve this double link inverted pendulum using Takagi-Sugeno Method. Firstly, You will find the Dynamic Equations of this system. Finding the premise variables you will design Fuzzy rules with consequent terms which is called State Equations. After that you will design system Matrices, Input(Control) Matrices, Output Matrices. There will be Midterm exam homework. Up to this point, the next ones will be Final homework, After Solving the state equations of each rule in MATLAB program, you will draw the curves of each state variables in MATLAB and interpret them.