New exponentially weighted inequality and its application to finite-time stability of descriptor time-delay systems

Abstract

The paper considers the finite-time stability of descriptor time-delay systems. Firstly, we establish a set of exponentially weighted orthogonal polynomials, and based on this, we obtain a new exponentially weighted inequality(EWI). Secondly, an augmented Lyapunov-like functional (LLF) is established driven by the presented EWI. Finally, by applying the EWI and the LLF, some sufficient conditions for ensuring the finite-time stability of the system are obtained. A small partial element equivalent circuit model and two numerical examples are used to verify the effectiveness of the method.