Improved Delay-Dependent Stability Analysis of Fixed-Point State-Space Digital Filters With Time-Varying Delay and Generalized Overflow Arithmetic

This paper is concerned with the stability analysis of fixed-point state-space digital filters with generalized overflow arithmetic and a time-varying delay. This paper aims to derive a delay and nonlinear function bound dependent asymptotical stability criterion with less conservatism. Firstly, a new Lyapunov functional with several augmented terms, including extra free matrices and overflow nonlinear function, is constructed such that it has a relaxed positive condition. Then, for bounding the summation term arising in the forward difference of Lyapunov functional, a new lemma is developed to introduce the terms for linking the delayed states and the overflow nonlinear function, the Wirtinger-based summation inequality and several zero-value terms are applied to add more cross terms. As a result, a stability criterion with less conservatism is established and its conservatism. Finally, several numerical examples are given to illustrate the advantages of the proposed method.