Hankel-like norm and its comparison with standard induced norm

This paper extends the concept of the Hankel-norm to a general one. The new induced norms presented in this paper, entitled as Hankel-like norms, are the gains of the standard linear time-invariant (LTIV) stable operator from past inputs to future outputs measured with various L^P-norms. Those are also associated with the worst initial conditions imposed by the norm-bounded past inputs to cause the maximal future output norms. Thus the worst initial conditions imposed by the unit norm inputs are also presented in this paper. The Hankel-norm turns out to be a special case of these new induced norms. For comparison, some standard induced norms are also derived