H∞ control with performance bound for a class of uncertain linear systems

H∞ control is studied for a class of uncertain linear systems when the uncertainty is assumed to exist in the state matrix. A decentralized control scheme with two observer-based feedback controllers is developed for such a class of uncertain linear systems with two control channels. The gains of the observer-based feedback controllers can be computed from the positive-definite solutions of the two Riccati-like algebraic equations with some tuning freedom. The resulting closed-loop system provides guaranteed stability and H∞-norm bounded performance in the presence of parameter uncertainty.