Parametric absolute stabilization of lurie time-delay systems with polytopic uncertainty based on state feedback

The paper investigates the parametric absolute stabilization problem for polytopic uncertainty Lurie time-delay systems with constant reference inputs and uncertain parameters based on state feedback. The concept of parametric absolute stabilization characterizes both the existence and the stability of equilibrium in the case of uncertain parameters shift. First, the conditions for existence are formulated to guarantee that the Lurie time-delay systems with polytopic uncertainty remains stable despite the shift of the equilibrium location caused by changes of uncertain parameters and reference inputs based on state feedback. Then, a delay-dependent stability condition in parametric stability region for Lurie time-delay systems is proposed based on linear matrix inequality. Finally, an example is given to illustrate the effectiveness of the proposed method.