Construction of input-output map realizations using differential forms

A problem of the dynamical system realization, i.e., a problem of constructing the state-space realization for input-output map, is solved. The known data concerning the existence of the realization without derivatives of controls are extended to the general case. The conditions of the existence of a state-space system with the fixed-order derivatives of control are obtained using methods of differential forms theory. Two algorithms for constructing realizations are offered. The first algorithm with introduction of new outputs is convenient for reducing the derivative order for one input without change in derivative orders of other outputs. The second algorithm is useful for reducing the derivative orders for several outputs. These algorithms may be used for decreasing the control derivative orders in the state-space system if we consider the system as input-output map. The example of the simplified model of a crane showing the effectiveness of this approach is considered.

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