Global Volterra Series for Nonlinear Meromorphic Systems on Complex Manifolds

A global Volterra series is obtained for an meromorphic systemdefined on a complex manifold c. Local bilinearizations arepieced together by a fibre bundle giving rise to a ‘twisted’bilinear system on c.     

On the inversion problem for nonlinear systems

A new homology technique is applied to the inversion problemfor nonlinear systems, both in the input—output and state-spaceformulations.     

On Nonlinear Perturbations of Dynamical Systems

The nonlinear variation-of-constants formula is generalizedto the case where the unperturbed operator has nonelliptic Fréchetderivation.     

Pseudo-linear systems, Lie algebras, and stability

The stability of pseudo-linear systems is considered by usinga diagonal-dominance approach coupled with the theory of semisimpleLie algebras and the Cartan decomposition     

Nonlinear systems, the Lie series, and the left shift operator: Application to nonlinear optimal control

A new representation of nonlinear systems involving the Lieseries is obtained and applied to nonlinear optimal control.     

On the inversion of the n-dimensional Laplace transform

In this paper we study the inversion of the multidimensionalLaplace transform by a combination of a general partial-fractionexpansion formula and the theory of residues. The ideas maybe applied to nonlinear systems defined by Volterra series.