Uniform Disturbance Attenuation for Markovian Jump Linear Systems in Discrete Time

A complete characterization of almost surely uniformly stable and contractive Markovian jump linear systems is given in the discrete-time domain via the union of an increasing family of linear matrix inequality conditions. This characterization draws on the facts that the Riccati difference inequality associated with a stable and contractive linear time-varying system admits a solution which has finite memory of past parameters, and that each Markovian jump linear system can be treated as a switched linear system where the underlying Markov chain defines the switching path constraint. The result leads to a semidefinite programming-based controller synthesis technique, from which optimal finite-path dependent dynamic output feedback controllers arise naturally.