Bounding the state covariance matrix for switched linear systems with noise

C. Klett, M. Abate, Y. Yoon, S. Coogan, E. Feron
American Control Conference, 2020

Abstract

This paper studies the infinite-time behavior of switched linear systems in the presence of additive noise. In particular, we show that the propagation of the state covariance matrix can be described by a linear affine system and therefore classified by an invariant region of the covariance space. An algorithm is presented for bounding the state covariance matrix with a suitable hyper-ellipsoid in the dimension of the covariance space; we form this algorithm using a Kronecker algebra-based derivation.