Finite-time stability and stabilization for linear time-varying descriptors systems

In this paper, two necessary and sufficient conditions are provided to assess the finite-time stability of descriptor systems. The first is based on the solution of a differential Lyapunov equation, while the second requires the solution of a feasibility problem with differential linear matrix constraints. While the first condition is numerically more efficient, the second is further exploited to derive a sufficient condition for finite-time stabilization via state feedback that requires only the dynamic part of the descriptor state. The effectiveness of the proposed approach is discussed by means of a numerical example.