Global stability analysis for discrete-time nonlinear systems

Developing computationally-efficient nonconservative stability analysis tools for generic nonlinear systems has eluded researchers for the past century. While this is a challenging problem, any nonlinear system can be approximated arbitrarily closely as a network of interconnections of linear systems and bounded monotonic nonlinear operators. A computational approach is developed for the stability analysis of such networks. The main stability analysis tool is formulated as a linear matrix inequality feasibility problem, which can be solved by ellipsoid or interior point algorithms. The nonlinear stability analysis tools are applied to artificial neural networks, which are nonlinear process modeling tools that have been heavily studied in the past ten years, and are the only generic black-box nonlinear models significantly used in the process industries. Ideas for future work are outlined.