State-feedback \(H_\infty\) control of nonlinear singularly perturbed systems (Q2771038)

This paper deals with the \(H_\infty\) control problem for an affine singularly perturbed system, which is nonlinear in the state variables. Under suitable assumptions on the linearized problem, one constructs \(\varepsilon\)-independent composite and linear controllers that solve the local \(H_\infty\) control problem for the full-order system for all small enough \(\varepsilon\). These controllers solve also the corresponding problem for the descriptor system.NEWLINENEWLINENEWLINEThe ``central'' nonlinear controller can be approximated in the form of expansions in the powers of \(\varepsilon\).NEWLINENEWLINENEWLINEAn illustrative example shows that the higher-order approximate controller achieves the best performance, while the composite (zero-order approximate) controller leads to a better performance than the linear one.