The Recursive Algorithm for H_∞ Type Riccati Equation with Small Parameter

Abstract

This paper considers new recursive algorithm to find the positive semidefinite stabilizing solution of H_∞ type Riccati equation with small parameter where the solution P depend on the ε. In order to obtain the stabilizing solution of the H_∞ type Riccati equation, we must solve the generalized algebraic Riccati equation. Using the recursive algorithm, we show that the solution of the generalized algebraic Riccati equation converges to a positive semidefinite stabilizing solution with the rate of convergence of O(ε^k).
We also show that for singularly perturbed systems, if the H_∞ norm of the transfer matrix function is less than the H_∞ norms for the fast system and for the reduced slow system, then the H_∞ type Riccati equation has a positive semidefinite stabilizing solution.