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Controller reduction preserving the closed-loop performance for a class of linear multivariable systems

In this paper, a new method of controller reduction preserving both stability and performance of the closed-loop system is proposed. First, a quadratic cost is introduced which represents a performance of the closed-loop system constructed by linear multivariable plant and high-order dynamic controller. Then the controller reduction problem is formulated as finding the fixed low-order dynamic controller preserving stability and value of the quadratic cost. Secondly, by using the Lyapunov equation, the problem is converted into the convex optimization problem with constraint described by a linear matrix inequality (LMI), and the sufficient condition for the existence of such an optimal reduced-order controller is shown. Finally, a numerical example is demonstrated.