A Finite Energy Property of Stable Inversion to Nonminimum Phase Nonlinear Systems

Stable inversion is a completely new approach to the output tracking control of nonminimum phase nonlinear systems. It not only offers exact reproduction of a given reference output trajectory but also guarantees stability of all external and internal signals. After a brief review of the stable inversion problem, the paper establishes a finite energy property of stable inverses. That is, out of infinitely many possible inverse solutions, the one provided by the stable inversion process is the only one that has finite energy, or, the L2( 1; +1)-norm. The effectiveness of the stable inversion approach in output tracking as compared with the well-known classic inversion and nonlinear regulation approaches is demonstrated by working out an example of a nonlinear nonminimum phase system.