  This paper studies the problem of online stabilization of an unknown
discrete-time linear time-varying (LTV) system under bounded non-stochastic
(potentially adversarial) disturbances. We propose a novel control algorithm
based on convex body chasing (CBC). Under the assumption of infrequently
changing or slowly drifting dynamics, the algorithm guarantees
bounded-input-bounded-output stability in the closed loop. Our approach avoids
system identification and applies, with minimal disturbance assumptions, to a
variety of LTV systems of practical importance. We demonstrate the algorithm
numerically on examples of LTV systems including Markov linear jump systems
with finitely many jumps.
