Strongly absolute stability of Lur´e-type discrete-time descriptor systems

This paper considers Lur´e-type discrete-time descriptor systems. First, the concept of strongly absolute stability is defined for Lur´e-type discrete-time descriptor systems. Such a notion is a generalization of absolute stability for Lur´e-type standard state-space systems. Then by using Lyapunov stability theory and linear matrix inequality (LMI), we derive LMI based circle criterion and Popov criterion for strongly absolute stability. Finally, a numerical example is given to illustrate the effectiveness of the obtained results.