Piecewise Linear Modeling

This book treats analysis and design of piecewise linear control systems. In this chapter, we lay the foundation for the analysis by presenting the mathematical model on which the subsequent developments will be based. We derive an explicit matrix representation of the model and discuss solution concepts. We extend modeling techniques for uncertain linear systems to piecewise linear systems and show how norm-bound uncertainties and smooth nonlinearities can be treated rigorously in this framework. Finally, we note that piecewise linear systems enjoy important interconnection properties that allow complex systems to be constructed from the interconnection of simpler subsystems, and discuss memory-efficient model representations.