On the strong stabilization problem and performance of stable ℋ∞ controllers

A strong stabilization problem is considered for MIMO finite dimensional linear time invariant systems. It is shown that if an algebraic Riccati equation (ARE) has a positive semi-definite solution, then a strongly stabilizing controller can be constructed using state space techniques. This controller is of the same order as the plant. Moreover, under this sufficient condition, a finite dimensional characterization of a fairly large set of strongly stabilizing controllers is obtained. Using a similar ARE, the authors (1996) constructed a stable suboptimal ℋ^∞ controller of order 2n, where n is the order of the generalized plant. The ℋ^∞ performance level attained by this controller is studied here. An alternative stable ℋ^∞ controller design method is also discussed