On stochastic linear systems with zonotopic support sets

Authors

• M.E. Villanueva, B. Houska

Reference

• Automatica
  Volume 111:108652, 2020.

Abstract

This paper analyzes stochastic linear discrete-time processes, whose process noise sequence consists of independent and uniformly distributed random variables on given compact zonotopes. We propose a cumulant-based approach for approximating both the transient and limit distributions of the associated state sequence. The method relies on a novel class of k-symmetric Lyapunov equations, which are used to construct explicit expressions for the cumulants. The state distribution is recovered via a generalized Gram-Charlier expansion with respect to products of a multivariate variant of Wigner's semicircle distribution using Chebyshev polynomials of the second kind. This expansion converges uniformly to the exact state distribution of the stochastic systems considered, under surprisingly mild conditions.

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