Algebraic Solution to H2 Control Problems. II. The Multivariable Decoupling Case

The control of multivariable systems with time delays is an important problem in linear control systems. The goal of this paper is to develop an algebraic design method for multivariable systems with multiple time delays. In the method, the algebra-based input-output design technique is adopted, because it is easy to understand and use, and it requires no state variables. We focus mainly on decoupled response. First, all stabilizing decoupling controllers are parametrized. Second, the optimal decoupling controller is derived by minimizing the sensitivity function. Finally, the performance and robustness are analyzed and a simple tuning rule is developed for quantitative performance and robustness. The most important feature of the proposed method is that the controller is optimal, analytical, and can provide decoupling response. Typical examples are provided to illustrate the proposed method.