It has been the standard teaching of today that backward stability analysis is taught as absolute, just as in Newtonian physics time is taught as absolute time. We will prove that it is not true in general. It depends on algorithms. We will prove that forward and mixed stability analysis are absolutely invalid stability analysis in the sense that they have absolutely wrong reference points for ...

It is shown that the assumption of D-stability of the interconnection matrix, together with the standard assumptions on the activation functions, guarantee the existence of a unique equilibrium under a synchronous mode of operation as well as a class of asynchronous modes. For the synchronous mode, these assumptions are also shown to imply local asymptotic stability of the equilibrium. For the ...