Controllability, observability and the jump linear quadratic problem in continuous time

This paper is concerned with the controllability and observability of continuous-time linear systems that possess randomly jumping parameters which can be described by finite-state Markov processes, and with the relationships between these properties and the solution of the infinite time jump linear quadratic (JLQ) optimal control problem. The solution of the continuous-time Markov JLQ problem with finite or infinite time horizons is known. In this paper a definition and algebraic test of controllability for continuous-time Markovian jump linear systems are given. This condition is related to the existence of finite cost steady-state JLQ solutions.