New iterative algorithm for algebraic Riccati equation related to H-infinity control problem of singularly perturbed systems

In this note, we present the solution to the algebraic Riccati equation (AR E) with indefinite sign quadratic term related to the H-infinity control pr oblem for singularly perturbed system by means of a Kleinman's type algorit hm. The resulting algorithm is very efficient from the numerical point of v iew because the ARE is solvable even if the quadratic term has an indefinit e sign. Moreover, the resulting iterative algorithm is quadratically conver gent. We also present a new algorithm for solving the generalized algebraic Lyapunov equation (GALE) on the basis of the fixed point algorithm.