First, three different but related output regulation performance criteria for the linear time-varying system are defined in the discrete-time domain, namely, the peak impulse response, peak output variance, and average output variance per unit time. Then they are extended for switched linear systems and Markovian jump linear systems, and characterized by an increasing union of finite-dimensional linear matrix inequality conditions. Finally, the infinite-horizon suboptimal LQG control problem, which aims to maintain the average output variance below a given level subject to the uniform exponential stability of the closed-loop system, is solved for both switched linear systems and Markovian jump linear systems; the solution is given by a dynamic linear output feedback controller that not only perfectly observes the present mode but also recalls a finite number of past modes.