Lurie Control Systems With Delays Robust Absolute Stability

In this paper, the problem of absolute stability of Lurie control systems is studied, and the main purpose is to discuss the robust absolute stability conditions for the Lurie control systems with time-delay. Some results obtained are improved and perfected.1. Deals with the problem of the absolute stability of Lurie control systems with time delay in control input. By constructing appropriate Lyapunov functional and combining the technique of analyzing inequality, delay-independent and delay-dependent conditions for the absolute stability of such systems are obtained. The derived sufficient conditions are expressed in terms of linear matrix inequalities(LMI) to find the less conservative criteria, which can be easily validated by Matlab Toolbox. Numerical examples are given to illustrate the effectiveness of the proposed method.2. Deals with delay-dependent robust stability of neutral Lurie control systems with multiple nonlinearities and time-varying structured uncertainties. The Lyapunov functional method is used. By adding some appropriate zero terms to the deviation of V and constructing some linear matrix inequalities. Then the delay-dependent absolute stability and robust stability sufficient conditions is derived. Finally, a numerical example is presented to illustrate the effectiveness of the method.3. The robust stability of uncertain neutral Lurie control systems with discrete and distributed delays is investigated. The uncertainties under consideration are norm bounded and possibly time varying. By constructing appropriate Lyapunov functional and combining the technique of analyzing inequality, the sufficient conditions for the absolute stability of such systems are derived. The proposed stability criterions are formulated in the form of a linear matrix inequality and it is easy to check the robust absolute stabilities. A numerical example is given to illustrate the effectiveness of the proposed method.4. The stability of Lurie control systems with multiple time-delays is investigated. The system with multiple time-delays is transformed, then a suitable Lyapunov functional is selected, the delay-dependent absolutely stable condition for Lurie control systems with multiple time-delays is obtained by applying the technique of analyzing inequality and the method of decomposing the matrices. The condition is based on the linear matrix inequality. Finally, a numerical example is given to demonstrate the derived condition is less conservative than those given in the literature.