Minimal realization in the max algebra is an extended linear complementarity problem
Systems & Control Letters
The extended linear complementarity problem
Mathematical Programming: Series A and B
Hybrid Systems Described by the Complementary Formalism
HART '97 Proceedings of the International Workshop on Hybrid and Real-Time Systems
On the Optimal Control Law for Linear Discrete Time Hybrid Systems
HSCC '02 Proceedings of the 5th International Workshop on Hybrid Systems: Computation and Control
Brief Equivalence of hybrid dynamical models
Automatica (Journal of IFAC)
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First we give a short description of the Extended Linear Complementarity Problem (ELCP), which is a mathematical programming problem. We briefly discuss how this problem can be used in the analysis of discrete event systems and continuous variable systems. Next we show that the ELCP can also be used to model and to analyze hybrid systems. More specifically, we consider a traffic-light-controlled intersection, which can be considered as a hybrid system. We construct a model that describes the evolution of the queue lengths in the various lanes (as continuous variables) as a function of time and we show that this leads to an ELCP. Furthermore, it can be shown that some problems in the analysis of another class of hybrid systems, the "complementary-slackness systems", also lead to an ELCP.