Solution of large generalized H∞ algebraic Riccati equations

Although synthesis of H∞ controllers via solution of algebraic Riccati equations (AREs) has been known for several decades, there is not a generally accepted algorithm that is suitable for large-scale systems. However, systems of large model order arise in a number of situations, for instance in approximation of partial differential equation models and power systems. Often the system descriptions are sparse when in generalized state-space form but not when converted to standard first-order form. An extension of a game-theoretic iterative algorithm to solve the H∞-algebraic Riccati equations for large generalized systems is presented. The highlight of this work is to preserve the sparse structure of the system description by using the generalized form instead of converting it into standard form. The proposed method is compared to other methods using several examples. It is shown that this method is accurate, even near optimal attenuation where the standard method cannot be used. The proposed method also performs well for a problem of structural control where other methods cannot be used. A method for calculating optimal attenuation that is significantly faster than the usual bisection procedure is also described.