Transfer matrix of the inverse model

Abstract Incremental true bond graphs are used for a matrix-based determination of first-order parameter sensitivities of transfer functions, of residuals of analytical redundancy relations, and of the transfer matrix of the inverse model of a linear multiple-input-multiple-output system given that the latter exists. Existing software can be used for this approach for the derivation of equations from a bond graph and from its associated incremental bond graph and for building the necessary matrices in symbolic form. Parameter sensitivities of transfer functions are obtained by multiplication of matrix entries. Symbolic differentiation of transfer functions is not needed. The approach is illustrated by means of hand derivation of results for small well-known examples. 

Let H denote the transfer matrix of the inverse model. Then... 

Symbolic Differentiation of the Transfer Matrix of the Inverse Model with Respect to a Parameter... 

Furthermore, if the linear inverse model of a linear MIMO model exists, equations from the bond graph of the direct model and the incremental bond graph of the inverse model can be automatically derived and matrices can be built. Computer algebra systems can be used to determine parameter sensitivities of the transfer matrix of the inverse model from these matrices. 

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