  Numerous state-feedback and observer designs for nonlinear dynamic systems
(NDS) have been developed in the past three decades. These designs assume that
NDS nonlinearities satisfy one of the following function set classifications:
bounded Jacobian, Lipschitz continuity, one-sided Lipschitz, quadratic
inner-boundedness, and quadratic boundedness. These function sets are
characterized by constant scalars or matrices bounding the NDS' nonlinearities.
These constants (i) depend on the NDS' operating region, topology, and
parameters, and (ii) are utilized to synthesize observer/controller gains.
Unfortunately, there is a near-complete absence of algorithms to compute such
bounding constants. In this paper, we develop analytical then computational
methods to compute such constants. First, for every function set
classification, we derive analytical expressions for these bounding constants
through global maximization formulations. Second, we utilize a derivative-free,
interval-based global maximization algorithm based on branch-and-bound
framework to numerically obtain the bounding constants. Third, we showcase the
effectiveness of our approaches to compute the corresponding parameters on some
NDS such as highway traffic networks and synchronous generator models.

Systems and Control;Systems and Control;Optimization and Control