Lurie Delay Systems Based On The Right To Freedom Of Matrix Absolute Stability

Lurie time-delay systems are a class of very important nonlinear systems; the problem of absolute stability for Lurie systems has been attracting much attention. As time-delays are frequently encountered in various systems, such as engineering systems, biological systems and economic system, and are often the sources of instability, the study of absolute stability for Lurie systems is of great theoretical meaning. In this dissertation, Lurie time-delay systems are investigated by employing the free-weighting matrix approach combined with methods of augmented Lyapunov- Krasovskii functional and retaining the terms ignored in the derivative of Lyapunov-Krasovskii functional in previous work, some less conservative delay-dependent absolute stability criteria are obtained.For Lurie systems with invariant time-delay, delay-dependent absolute stability criteria are obtained and formulated in the form of linear matrix inequalities (LMIs) by using augmented Lyapunov- Krasovskii functional combined with the free-weighting matrix approach. The criteria are then extended to the analysis of the robust absolute stability for Lurie systems with time-varying structured uncertainties.For Lurie systems with time-varying delay, an integral term was ignored when dealing with the derivative of Lyapunov-Krasovskii functional in previous work. In this dissertation, delay-dependent absolute stability criteria are obtained by applying free-weighting matrix approach without ignoring the useful integral term.For Lurie time-delay systems of neutral type, the absolute stability of neutral Lurie systems with a time-varying discrete-delay is investigated by using free-weighting matrix approach and considering the ignored term in previous work firstly. Then, delay-dependent absolute stability criteria for neutral Lurie systems with identical discrete- and neutral-delays and with different discrete- and neutral-delays are obtained respectively by using augmented Lyapunov functional combined with the free-weighting matrix approach. Finally, a summary of study on absolute stability of Lurie time-delay systems based on free-weighting matrix approach is presented, and prospects for further studies are mentioned.