Design of H2 Controller for a Class of Discrete Time-Delay Systems with the Closed-loop Pole Constraints

In this paper, the H₂ control for a class of discrete time-delay systems with the closed-loop pole constraints is considered. By employing LMI approach, the problem can be transformed to a convex optimal problem with constraints that is easy to be calculated. The obtained controller not only guarantees all the closed-loop poles to be placed inside a specified region, but also provides an H₂ performance upper bound. In particular, the obtained results are delay-dependent, and therefore, have less conservativeness. Numerical examples are given to illustrate the validity of the proposed method.