Invertibility of Observable Multivariable Nonlinear Systems
Based on the algorithm of Hirschorn  for obtaining inverses, sufficient conditions for invertibility of observable multivariable nonlinear systems are derived. For observable and invertible systems, a static left-inverse system is constructed. For certain noninvertible systems, the sufficient condition yields a characterization of input space on which the input-output map is injective.
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Singh, S. N.
Invertibility of Observable Multivariable Nonlinear Systems.
IEEE Transactions on Automatic Control, AC-27(2),