Optimal Disturbance Attenuation for Discrete-Time Switched and Markovian Jump Linear Systems

An exact condition for uniform stabilization and disturbance attenuation for switched linear systems is given in the discrete-time domain via the union of an increasing family of linear matrix inequality conditions. Associated with each Markovian jump linear system is a switched linear system, so we obtain a necessary and sufficient condition for almost sure uniform stabilization and disturbance attenuation for Markovian jump linear systems as well. The results lead to semidefinite programming–based controller synthesis techniques, from which optimal finite-path-dependent linear dynamic output feedback controllers arise naturally. In particular, under the notion of path-by-path optimal disturbance attenuation, finite-path-dependent controllers can outperform the usual modedependent ones.