Extended Dissipativity Analysis and Synthesis for Discrete-Time Lur'e Delayed Systems: Matrix-Separation-Based Lyapunov Functional Method

Abstract

This paper develops a matrix-separation-based Lyapunov functional method to study the extended dissipativity analysis and synthesis issue of discrete-time Lur'e-type delayed systems. The advanced idea of matrix-separation is reflected in Lyapunov functional candidates and estimates summation terms as precisely as feasible. First, we introduce a novel summation inequality based on the matrix-separation method to provide a bound for the augmented summation that involves common state variables. An improved delay-product-type Lyapunov functional is devised by extending non-positive definite summations as separate subblocks of the state-augmented summation. Then, by using the matrix injection method to handle the cubic delay term in the functional forward difference, a delay-variation-dependent stability criterion and an extended dissipativity criterion are developed under the matrix-separation-based method. Subsequently, sufficient conditions for the control design of Lur'e-type systems are derived. Finally, the effectiveness and superiority of the proposed method are verified through its application to Chua's circuits, neural networks, and a stochastic numerical example.