H2 and Mixed-Hz/H, Stable Stabilization

In certain applications the use of stable compensators greatly simplifies controller testing and implementation. Unfortunately, standard LQG theory, as well as mixednorm H2/H, theory, may yield compensators that are unstable. The problem of synthesizing stable stabilizing controllers has been of interest for many years [14], and a variety of techniques have been proposed based on modifications of existing synthesis methods to ensure stable compensation [3, 4, 9-13]. In particular, in 17, 9-13] the authors guarantee suboptimal strong stabilization by modifying standard LQG theory. In this paper we present several new modifications of the closed-loop Lyapunov equation for H2 theory and the closed-loop Riccati equation for H2/H, theory to guarantee controller stability prior to carrying out the optimization over the controller gains. Hence the present frame work generalizes the a priori approach developed in [lo, 12, 131 for constructing stable compensators with closedloop system satisfying H2 and H2/H, performance constraints.