On Necessary and Sufficient Conditions for ${H}_{\infty }$ Output Feedback Control of Markov Jump Linear Systems

This note addresses the output feedback H
_infin
control problem for continuous-time Markov jump linear systems. It is shown that the feasibility of a certain set of linear matrix inequalities is both sufficient and necessary for the existence of a solution. Under standard assumptions, we also give a Riccati-type sufficient and necessary condition for an H
_infin
-suboptimal controller to exist.