Invertibility of Observable Multivariable Nonlinear Systems
IEEE Transactions on Automatic Control
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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),