Robust stability and disturbance attenuation for a class of uncertain singularly perturbed systems

This paper considers the problem of robust stabilization and disturbance attenuation for a class of uncertain singularly perturbed systems with norm-bounded nonlinear uncertainties. It is shown that the state feedback gain matrices can be determined to guarantee the stability of the closed-loop system for all ε ϵ(0,∞). Based on this key result and some standard Riccati inequality approaches for robust control of singularly perturbed systems, a constructive design procedure is developed. For simplicity, the results are presented on the two-time-scale case; the extension of the results to multiple-time-scale is, however, straightforward.