H2-suboptimal stable stabilization

We present new results that are in the spirit of Halevi, Bernstein and Haddad (1991), Jacobus (1990) and Jacobus et al. (1990). Specifically, in these references the authors modify full- and reduced-order LQG theory to obtain suboptimal controllers that are stable. The new results given herein are based upon two different modifications of LQG theory that offer advantages over these earlier approaches. The first approach is based upon an a posteriori modification of LQG theory in the vein of Halevi, Bernstein and Haddad (1991). Unlike the technique of Halevi, Bernstein and Haddad, our modification of LQG theory involves a third equation coupled to the regulator Riccati equation. The advantage of our approach over Halevi, Bernstein and Haddad is a unified treatment of the reduced-order case. Our second approach involves an a priori modification to LQG theory (that is, prior to optimization) in the vein of Jacobus (1990) and Jacobus et al. (1990). Our approach is an improvement over the approach of Jacobus in that the modification to the design equations is less conservative