Recursive algorithm for mixed H-2/H-infinity control problem of singularlyperturbed systems

In this paper, we study the mixed H-2/H-infinity control problem for infini te-horizon singularly perturbed systems. In order to solve the problem, we must solve a pair of parametrized cross-coupled algebraic Riccati equations with a small positive parameter epsilon. Firstly, we solve the parametrize d cross-coupled algebraic Riccati equations using a Lyapunov iteration appr oach. Sufficient conditions are provided such that the proposed Lyapunov it erations converge to a positive semidefinite solution. Secondly, we propose a new algorithm, which combines Lyapunov iterations and recursive techniqu es together, to solve the parametrized cross-coupled algebraic Riccati equa tions. The new algorithm ensures that the solution of the parametrized cros s-coupled algebraic Riccati equations converges to a positive semidefinite solution with the rate of convergence of O(epsilon (k) ). As another import ant feature of this paper, our method is applicable to both standard and no n-standard singularly perturbed systems.