Recursive approach of H control problems for singularly perturbed systems under perfect- and imperfect-state measurements

In this paper, we study the H control problem for singularly perturbed systems under both perfect- and imperfect-state measurements by using the recursive approach of Gacjic et al. We construct a controller that guarantees a disturbance attenuation level larger than a boundary value of the reduced-order slow and fast subsystems when the singular perturbation parameter epsilon1 approaches zero. In order to obtain the controller, we must solve the generalized algebraic Riccati equations. The main results in this paper are to propose a new recursive algorithm to solve the generalized algebraic Riccati equations and to find sufficient conditions for the convergence of the proposed algorithm. 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(epsilon1k) under sufficient conditions. Furthermore, in the case of perfect-state measurements, we also show that the controller...