State-feedback H control of nonlinear singularly perturbed systems

We study the H control problem for an a$ne singularly perturbed system, which is nonlinear in the state variables. Under suitable assumptions on the linearized problem, we construct -independent composite and linear controllers that solve the local H control problem for the full-order system for all small enough . 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 . An illustrative example shows that the higher-order approximate controller achieves the better performance, while the composite (zeroorder approximate) controller leads to the better performance than the linear one. Copyright 2001 John Wiley & Sons, Ltd.