Relationship between the trace and maximum eigenvalue norms for linear quadratic control design

The use of a sum of squares H₂ norm is considered for optimal control system design. The relative advantages of the linear-quadratic-Gaussian (LQG) (trace norm) and the H_∞ (sup norm) cost functions are discussed. An argument is presented to show that the sum of squares norm (SSN) problem might be considered alongside the LQG and H_∞ cost problems. When exploring the relationship between the LQG and SSN problems, it is found that an LQG controller could be found which correspond to an SSN problem with larger disturbance inputs. This suggests that the LQG controller can be computed with the knowledge that it minimizes a well-defined SSN problem with worst-case uncertainty or disturbances. The range of a certain set of eigenvalues is found to provide a measure of the difference between the LQG and SSN problem designs