State-feedback H_∞ control of nonlinear singularly perturbed systems

We study the H_∞ control problem for an affine singularly perturbed system, which is nonlinear in the state variables. Under suitable assumptions on the linearized problem, we construct ε-independent composite and linear controllers that solve the local H_∞ control problem for the full-order system for all small enough ε. These controllers solve also the corresponding problem for the descriptor system. The 'central' nonlinear controller can be approximated in the form of expansions in the powers of ε. An illustrative example shows that the higher-order approximate controller achieves the better performance, while the composite (zero-order approximate) controller leads to the better performance than the linear one.