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

Nonlinear Dynamic Systems Parameterization Using Interval-Based Global Optimization: Computing Lipschitz Constants and Beyond