Stability analysis and design of time-delay uncertain systems using robust reliability method

A robust reliability method for stability analysis and reliability-based stabilization of time-delay dynamic systems with uncertain but bounded parameters is presented by treating the uncertain parameters as interval variables. The performance function used for robust reliability analysis is defined by a delayindependent stability criterion. The design of robust controllers is carried out by solving a reliability-based optimization problem in which the control cost satisfying design requirements is minimized. This kind of treatment makes it possible to achieve a balance between the reliability and control cost in the design of controller when uncertainties must be taken into account. By the method, a robust reliability measure of the degree of stability of a time-delay uncertain system can be provided, and the maximum robustness bounds of uncertain parameters such that the time-delay system to be stable can be obtained. All the procedures are based on the linear matrix inequality approach and therefore can be carried out conveniently. The effectiveness and feasibility of the proposed method are demonstrated with two practical examples. It is shown by numerical simulations and comparison that it is meaningful to take the robust reliability into account in the control design of uncertain systems.