SIAM Journal on Control and Optimization, Vol.32, No.3, 635-647, 1994
On the Game Riccati-Equations Arising in H(Infinity) Control-Problems
In the state-space approach to H(infinity) optimal control, feasible closed-loop gains gamma are characterized via a pair of game Riccati equations depending on gamma. This paper is concerned with the properties of these equations as gamma varies. The most general problem is considered (D11 not-equal 0) and the variations of the Riccati solutions are thoroughly analyzed. Insight is gained into the behavior near the optimum and into the dependence on gamma of the suboptimality conditions. In addition, concavity is established for a criterion that synthesizes the three conditions X greater-than-or-equal-to 0, Y greater-than-or-equal-to 0, and rho(XY) < gamma2. This suggests a numerically reliable Newton scheme for the computation of the optimal gamma. Most results presented here are extensions of earlier contributions. The main concern is to provide a complete and synthetic overview as well as results and formulas tailored to the development of numerically sound algorithms.