LINEAR MARKOV APPROXIMATIONS FOR PIECEWISE LINEAR STOCHASTIC SYSTEMS.

This paper is concerned with an approximate linear switched-parameter Markov model for discrete-time systems whose nonlinear homogeneous part is piecewise linear. A scalar system with white Gaussian noise input is considered and it is shown that a steady-state approximation is valid for two extreme cases. The first is the case when all the slopes of the piecewise linear model are stable, and the regions are large relative to the noise variance. The second is the case when there are unstable regions adjoining stable regions, and the unstable regions are small relative to the noise variance.