We show that the problem of finding a singular value decomposition of a matrix in the extended max algebra can be reformulated as an Extended Linear Complementarity Problem. This allows us to compute all the max-algebraic singular value decompositions of a matrix. This technique can also be used to calculate many other max-algebraic matrix decompositions.

We show that the Extended Linear Complementarity Problem (ELCP) can be recast as a standard Linear Complementarity Problem (LCP) provided that the surplus variables or the feasible set of the ELCP are bounded. Since many extensions of the LCP are special cases of the ELCP, this implies that these extensions can be rewritten as an LCP as well. Our equivalence proof is constructive and leads to t...

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 ...

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-controlle...

We consider the linear complementarity problem with uncertain data modeled by intervals, representing range of possible values. Many properties (such as solvability, uniqueness, convexity, finite number solutions etc.) are reflected constraint matrix. In order that has desired even in environment, we have to be able check them for all realizations interval data. This leads us robust matrices. p...