A new simplified behavior theory is proposed to address inversion-based control for linear, nonminimum-phase SISO systems. The chosen space of signals is the set of piecewise C∞-functions and input–output pairs (as weak solutions) satisfy a differential–integral equation with additional smoothness requirements. A related key result is the output–input (or inverse) representation of the behavior set that leads to the solution of a general stable inversion problem where polynomially unbounded, noncausal desired outputs are allowed. It is shown that this problem has a solution if and only if the smoothness degree of the desired output is greater than or equal to the system relative degree minus one. When this straightforward condition is satisfied, a closed-form expression provides the inverse input. Then, an analysis on preaction and postaction control follows. Two examples are included showing the relevance of output signal design in control applications.
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