Nonlinearity Measures for Distributed Parameter and Descriptor Systems

Abstract Control design and state estimation are usually more straightforward for linear than for nonlinear dynamical systems, which has motivated the development of methods for quantifying the extent of nonlinearity in dynamical systems. Although many well-defined methods have been proposed for systems described by ordinary differential equations, such methods are not as well explored for dynamical systems described by PDEs and descriptor systems that represent most chemical processes. This paper reviews, discusses, and compares methods for the definition and computation of nonlinearity measures. The measures are categorized in terms of open- vs. closed-loop control topologies, theoretical vs. numerically computed, state transformation dependency, input scaling dependency, linearization vs. optimized linear modeling vs. average linear modeling, applicability to unstable dynamical systems, and applicability to the right-hand side of the state equation or to input-output relationships. Then extensions of the nonlinearity measures are discussed for hybrid systems and those described by coupled differential, integral, and algebraic equations, often referred to as descriptor/singular systems.