Finite-time stability of uncertain singular systems based on time-varying Lyapunov function

This paper addresses the finite-time stability (FTS) and $H_{\infty}$ FTS of uncertain singular systems. At first, a class of time-dependent Lyapunov functions are constructed by using the convex combination method, and a class of zero terms with a convex combination of freely weighted matrices are introduced to get the desired results. Then the new explicit sufficient conditions for FTS and $H_{\infty}$ FTS of the uncertain singular systems are given by using LMI. These conditions guarantee the regularity and impulse-free of the uncertain singular systems. Finally, by using the LMI toolbox in the MATLAB, two numerical examples are given to verify the validity of the developed results.