Abstract
In this paper, we develop distributed H 2 semistability theory for linear dynamical systems. Using this theory, we design distributed H 2 optimal semistable controllers for linear dynamical systems. Unlike the standard H 2 optimal control problem, a complicating feature of the distributed H 2 optimal semistable stabilization problem is that the closed-loop Lyapunov equation guaranteeing semistability can admit multiple solutions. Necessary and sufficient conditions for existence of solutions to the semistable Lyapunov equation are derived and a design framework for distributed optimal controllers is presented.
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