Piecewise linear Markov chains and analysis of their stability

Piecewise linear functions and piecewise linear operators are defined, some of their properties are studied. A class of piecewise linear Markov chains is introduced by means of the notion of piecewise linear operator. A stability problem for these chains is solved by virtue of the Lyapunov function method. Some examples of piecewise linear Markov chains describing queueing systems are considered.