New iterative algorithm for algebraic Riccati equation related to H/sub ∞/ control problem of singularly perturbed systems

We present the solution to the algebraic Riccati equation (ARE) with indefinite sign quadratic term related to the H/sub /spl infin// control problem for singularly perturbed systems by means of a Kleinman type algorithm. The resulting algorithm is very efficient from the numerical point of view because the ARE is solvable even if the quadratic term has an indefinite sign. Moreover, the resulting iterative algorithm is quadratically convergent. We also present an algorithm for solving the generalized algebraic Lyapunov equation on the basis of the fixed point algorithm.