TABLE OF CONTENTS Let us consider the behavior of the control function u( t) and the state vector X( t) of the system (7.1) (7.2), given that the desired reference input-controlled output map assigned by (7.25) is satisfied.
Assume henceforth that equidimensional input and output vectors of the system (7.1) (7.2) are considered, i.e., that m = p.
From (7.28) it follows that the function
| (7.29) |  |
uniquely satisfies (7.27) and is the solution of the nonlinear inverse dynamics. By substituting (7.29) into the state equation (7.1), we obtain
| (7.30) |  |
The system (7.30) describes the behavior of the state vector X( t) of the system (7.1) (7.2), given that the desired output behavior assigned by (7.25) is fulfilled.
It is easy to see that (7.29) (7.30) and the inverse system equations (7.21) (7.22) are the same. So, the boundedness of the NID-control function (7.29) corresponds to bounded-input-bounded-output (BIBO) stability of the inverse system (7.21) (7.22). Related remarks can be found in [Silverman (1969) ; Porter (1970) ; Fomin et al. (1981) ].
If the nonlinear inverse dynamics solution u NID( t) of (7.29) is an unbounded function, i.e.,
then the desired output behavior assigned by the reference model (7.25)
is unrealizable in the system (7.1) (7.2) where t ? [ t 0, ?). This is because the increase in the control function u NID( t) leads inevitably to saturation of the control variables in...
