Recursive approach of H-infinity control problems for singularly perturbedsystems under perfect- and imperfect-state measurements

In this paper, we study the H-infinity control for singularly perturbed sys tems under both perfect- and imperfect-state measurements by using the recu rsive 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 eps ilon 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 Ri ccati equations and to find sufficient conditions for the convergence of th e proposed algorithm. Using the recursive algorithm, we show that the solut ion of the generalized algebraic Riccati equation converges to a positive s emidefinite stabilizing solution with the rate of convergence of O(epsilon( k)) under sufficient conditions. Furthermore, in the case of perfect-state measurements, we also show that the controller achieves the performance lev el gamma + O(epsilon(k+1)). In addition, we do not assume here that A(22) i s non-singular. Therefore, our new results are applicable to both standard and non-standard singularly perturbed systems, Finally, in order to show th e effectiveness of the proposed algorithm, numerical examples are included.