New results of robust quadratically stabilizing control for uncertain linear time-delay systems

The problem of robust quadratic stabilization for a class of uncertain linear dynamic systems with time-delays in both state and control is discussed in this paper. The uncertain time-delay systems under consideration are described by state differential equations with unknown-but-bounded uncertain parameters that are confined into convex polyhedrons. A new necessary and sufficient condition for the existence of quadratically stabilizing control law and the corresponding synthesis method are derived, the results are given in terms of a set of linear matrix inequalities (LMIs). Finally, numerical examples are presented to demonstrate the effectiveness of the obtained results.