How to compare power requirements for different control design approaches?
There are norms that can be used to "measure" (also to compare) signals (\$L_1\$, \$L_2\$ and \$L_{\infty}\$) and systems (\$H_2\$ and \$H_{\infty}\$) for SISO and MIMO cases. There are deterministic and stochastic interpretations for it. For example, \$H_2\$ norm of a stable system \$H\$ is the root-mean-square of the impulse response of the system. In stochastic terms, the \$H_2\$ norm measures the steady-state covariance (or power) of the output response \$y = H\omega\$ to unit white noise inputs \$\omega\$. Specifically in Matlab, n = norm(sys) or n = norm(sys,2) returns the root-mean-squares of the impulse response of the linear dynamic system model sys. For a signal \$x\$, the \$L_2\$ norm represents the total energy (use norm(x,2)). In other hand, the RMS value is associated with the average power. In this case, you can use the rms function in Matlab.