On the non-optimality of linear quadratic gaussian balanced truncation for constrained order controller design

\u3cp\u3eFor model based control designs like boldsymbol{H}{2} and boldsymbol{H}{ boldsymbol{ infty}} optimal control, the controller order is typically equal to the model order. However, the synthesis and real-time implementation of these controllers may be hampered for models of large order due to computational limitations. Several closed-loop relevant order reduction techniques have been developed in order to overcome this problem. One technique is Linear Quadratic Gaussian (LQG) balanced truncation, which is closely related to LQG and boldsymbol{H}{2} optimal controller design. This paper demonstrates the non-optimality of this technique for constrained order boldsymbol{H}{2} optimal controller design. Furthermore, improvements to reduce the loss of performance as a result of truncation are proposed. These improvements can be applied to a large class of controller designs and order reduction techniques as well.\u3c/p\u3