H2 optimal semistable control for linear dynamical systems: An LMI approach

In this paper, we develop H2 semistability theory for linear dynamical systems. Using this theory, we design H2 optimal semistable controllers for linear dynamical systems. Unlike the standard H2 optimal control problem, a complicating feature of the H2 optimal semistable stabilization problem is that the closed-loop Lyapunov equation guaranteeing semistability can admit multiple solutions. An interesting feature of the proposed approach, however, is that a least squares solution over all possible semistabilizing solutions corresponds to the H2 optimal solution. It is shown that this least squares solution can be characterized by a linear matrix inequality minimization problem.