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where the deviation variables (Eq. 4.60) are defined using xss = xo,t and Yss = Yo,i and the elements of the Jacobian matrices are derived by evaluating the derivatives of f and g at the corresponding operating point (xo,i,yo,t) such that

0f dx

A linear time-varying global model is constructed by using the local models to approximate the nonlinear dynamics of a batch run. The time-varying model is obtained by interpolating between local models by using model validity functions Pi(t) which are similar to the interpolation function u>i of Eq. 4.114. Model validity functions are the estimates of the validity of various local models in different operating points and for N local models

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