Inversion algorithm for recursive nonlinear systems (Q2704997)

The purpose of this paper is to study the right invertibility problem for a nonlinear system (called recursive nonlinear system (RNS)) described by a higher-order difference equation relating the inputs, outputs and a finite number of their time-shifts: NEWLINE\[NEWLINE y(t) = F(y(t - 1),\dots , y(t - \mu), u(t - 1),\dots , u(t - \nu)). NEWLINE\]NEWLINE Right invertibility means the possibility of generating a prespecified sequence at system output by suitably choosing the input sequence. In the study the author follows the approach where the notion of rank plays the key role. This notion was introduced by Fliess for continuous-time systems and is extended to RNS. It is shown that the inversion algorithm provides the means to compute the rank of the system. Necessary and sufficient conditions for local right invertibility in terms of the rank of the system are proposed.