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


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.