  Nonlinear dynamic systems can be classified into various classes depending on
the modeled nonlinearity. These classes include Lipschitz, bounded Jacobian,
one-sided Lipschitz (OSL), and quadratically inner-bounded (QIB). Such classes
essentially yield bounding constants characterizing the nonlinearity. This is
then used to design observers and controllers through Riccati equations or
matrix inequalities. While analytical expressions for bounding constants of
Lipschitz and bounded Jacobian nonlinearity are studied in the literature, OSL
and QIB classes are not thoroughly analyzed---computationally or analytically.
In short, this paper develops analytical expressions of OSL and QIB bounding
constants. These expressions are posed as constrained maximization problems,
which can be solved via various optimization algorithms. This paper also
presents a novel insight particularly on QIB function set: any function that is
QIB turns out to be also Lipschitz continuous.
