Monotonicity and convexity of H/sup /spl infin// Riccati solutions in general case

State space formulas for H/sup /spl infin// optimal control problem involve two H/sup /spl infin// Riccati equations, whose solutions can be used to construct an optimal or suboptimal H/sup /spl infin// controller. This paper studies the existence of the solutions to the two H/sup /spl infin// Riccati equations in Glover-Doyle's formulation which is the most general one yet been considered, and shows that the solutions are nonincreasing convex functions in the domain of interest. The monotonicity and convexity of those H/sup /spl infin// Riccati solutions guarantee that the spectral radius of the product of those two Riccati solutions is also a nonincreasing convex function of /spl gamma/ in the domain of interest. According to these properties, a quadratically convergent algorithm is developed to compute the optimal H/sup /spl infin//.