Robust Stability of Singularly Perturbed Descriptor Systems With Nonlinear Perturbation

This technical note is concerned with the problem of robust stability of singularly perturbed descriptor systems with nonlinear perturbation. We first use the fixed-point principle to investigate the existence of the solution for the given singularly perturbed system, a linear matrix inequality condition is obtained for the existence and uniqueness of the solution. In addition, a sufficient condition is presented via linear matrix inequality under which the solution exists and is globally exponentially stable simultaneously. The criterion presented in this technical note is independent of the small parameter and the stability bound can be derived efficiently. Finally, the approach is illustrated by two numerical examples.