Qualitative Analysis of Nonlinear Parameterized Systems. Part 1: NonlinearSystems Representation and Dynamical Systems Theory

摘要

The analysis of parameterized nonlinear models is considered and a new approachis introduced which provides a framework for the global analysis of both continuous and discrete time nonlinear systems. The paper is divided into two parts. An overview of nonlinear system representations and dynamical systems theory is provided in part one, which forms the basis for the results in the second part. The latter introduces a numerically based analysis tool and demonstrates that this provides a flexible framework for the analysis of a diverse range of nonlinear model types. It is shown, by extending the numerical algorithm, that the approach provides a global perspective to the results that is difficult to obtain using analytical methods alone. Simple examples are used to illustrate how the new approach provides both qualitative information and a global perspective over a defined region of the systems parameter space. The method proves to be a powerful tool when used to probe the nonlinear characteristic of a system.