A graphical analysis method for piecewise linear systems

This paper fuses ideas from computational geometry, network theory and linear systems theory in order to develop a new tool for piecewise linear systems analysis. Specifically system models with piecewise linear functions such as saturation, relay and dead zones are represented as directed connected node graphs that capture information concerning the system´s global dynamics. Logic, such as rules within a rule-based controller, can also be mapped into the node graph of the system, thus showing the interaction between the logic and the system dynamics. The node graph is reminiscent of a phase portrait in that it gives a graphical representation that can aid analysis and potentially design. Unlike the phase portrait, the method is applicable to system models of more than two states. As a consequence, piecewise linear systems of arbitrary order may be studied and their stability patterns revealed