Generalized Linear Complementary Problems and the Analysis of Continuously Variable Systems and Discrete Event Systems

We present an overview of our research on the use of generalized linear complementarity problems (LCPs) for analysis of continuously variable systems and discrete event systems. We indicate how the Generalized LCP can be used to analyze piecewise-linear resistive electrical circuits. Next we discuss how the Extended LCP can be used to solve some fundamental problems that arise in max-algebraic system theory for discrete event systems. This shows that generalized LCPs appear in the analysis and modeling of certain continuously variable systems and discrete event systems. Since hybrid systems exhibit characteristics of both continuously variable systems and discrete event systems, this leads to the question as to whether generalized LCPs can also play a role in the modeling and analysis of certain classes of hybrid systems.