Abstract
This chapter is divided into two sections. In the first section, we consider that a generalized adjoint system is one to one and onto when the original system is, and vice versa. In the second section, the invertibility of an input–output system by its generalized adjoint system is considered.
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- 1.
An alternative to (6.5) and (6.22) are \(A^{\#}(u)(t) =\delta (u_{t} - u_{t}^{\#}) \cdot \zeta (t)\) and \(G(A^{\#})(y)(t) =\delta (y_{t} -\tilde{ F}_{t}(u_{t}^{\#})) \cdot \zeta (t)\) where \(\delta: U_{t} \rightarrow \mathfrak{R}\) is the delta function, that is δ(u t ) = 1 if u t is zero and = 0 else. This A # is bounded, but not continuous; however, the equivalence relation in the invertibility calculation becomes an equality.
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Serakos, D. (2015). On Invertibility Using the Generalized Adjoint System. In: Generalized Adjoint Systems. SpringerBriefs in Optimization. Springer, Cham. https://doi.org/10.1007/978-3-319-16652-0_6
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