  In this work, we consider the dynamics of repairable systems characterized by
three distinct states: one signifying normal operational states, another
representing degraded conditions and a third denoting failed conditions. These
systems are characterized by their ability to be repaired when failures and/or
degradation occur. Typically described by transport equations, these systems
exhibit a coupled nature, interlinked through integro-differential equations
and integral boundary conditions that dictate the transitions among all the
states. In this paper, we address two less-explored facets: 1) the
well-posedness and the asymptotic behavior of such systems with maximum repair
time being finite; and 2) the bilinear controllability of the system via repair
actions. In particular, we focus on the case where only one degraded and one
failed states exist. We first discuss part 1) for given time-independent repair
rates and then design the space-time dependent repair strategies that can
manipulate system dynamics to achieve the desired level over a finite horizon.
Our objective is to enhance the system availability -- the probability of being
operational when needed over a fixed period of time. We present rigorous
analysis and develop control strategies that leverage the bilinear structure of
the system model.
