Η∞ State-feedback control of nonlinear singularly perturbed systems

We study the H_∞ control problem for an affine singularly perturbed system, which is nonlinear not only in the slow variable (as in the standard case), but also in the fast variable. We construct an e-independent composite controller by solving a slow partial differential equation, that corresponds to the reduced Hamiltonian system, and by solving a fast partial differential equation. The composite controller solves the local H_∞ control problem for all small enough ε. It solves also the corresponding problem for the descriptor system. We obtain an asymptotic approximation of the optimal controller and of the solution to Hamilton-Jacobi equation.