Linear Markov Approximations of Piecewise Linear Stochastic Systems

This paper is concerned with the properties of piecewise linear discrete-time dynamic systems driven by white Gaussian noise. The properties of the deterministic system are explored, and condition for the existence of invariant distributions are derived. The existence of an invariant distribution was then used to justify the approximation of the stochastic system by a switched Markov linear model if the piecewise linear regions are large “contracting” ones or small “expanding” ones relative to the input noise variance. The approach is expected to be useful for constructing approximate nonlinear filtering schemes for such systems.