Stabilisation of uncertain singularly perturbed systems

This note studies the robust stabilisation problem of a linear time-invariant singularly perturbed system with nonlinear uncertainties, where the only information available for system uncertainties is their norm upper bounds, and no matching conditions are assumed. A linear stabilising control law is presented which can be determined by the solutions of two independent Lyapunov equations. The system stability bound can then be obtained by using the existing methods. Finally, a numerical example is given to illustrate the applications of the proposed results, and future work on this subject is also discussed.