An analysis method for piecewise linear dynamical systems

Abstract

A wide range of nonlinear dynamical systems contain abrupt changes in system behaviour and are often controlled using some kind of logic such as a rule-base. These changes in the system dynamics or controller actions make such systems intractable to conventional methods of systems analysis. By assuming all system nonlinearities can be represented as piecewise linear functions, a graphical analysis technique reminiscent of a phase portrait is developed for this class of systems and controllers. The state space of the system model is mapped into a directed node graph that captures the possible dynamic paths through the system. The paths found are directly related to the piecewise linear system functions or logic rules that created them. This node graph provides a graphical representation of the system that, like the phase portrait, captures the global dynamics of the system. The major difference is that the node graph generalises the phase portrait idea to systems of arbitrary dimensions.