Stabilization for a class of rectangular descriptor systems via time delayed dynamic compensator

This paper focuses on the stabilization problem for a class of rectangular descriptor systems through dynamic compensation. Such class of systems may not be stabilized by delay-free dynamic compensators, while delayed dynamic compensator could achieve such purpose. We provide a design scheme of time-delayed dynamic compensator which makes the closed-loop system admissible. The design involves solving a quadratic matrix inequality, and consequently, we build a linear matrix inequality (LMI) based algorithm to compute compensator gains. We verify that, under certain circumstances for which delay-free dynamic compensators fail to stabilize, the proposed method works well. An illustrative example demonstrates the usefulness of the present scheme.