Stability and guaranteed cost control for uncertain time-delay Lur'e systems

The problem of delay-dependent stability and guaranteed cost control (GCC) for a class of uncertain time-delay Lur'e systems are studied. By using an improved integral inequality, a less conservative delay-dependent stability criterion is formulated as the feasibility problem of the linear matrix inequality (LMI). The criterion is proved theoretically to be less conservative than some existing results for linear time-delay systems. Because of the fact that the matrices in the LMI-based stability criteria usually have different dimensions, different structures, and different variables, the conservatism analysis of the criteria is difficult. This study brings about a new insight into the comparison of conservatism among different stability criteria, which are expressed in certain LMI forms. The existence of the guaranteed cost controller is given in terms of matrix inequalities. The condition can be solved by using an iterative procedure and does not need any parameter tuning. A numerical example is given to illustrate the effectiveness of the proposed method.