I'm reading an introductionary article about LQR controller design. In the article is stated that goal of LQR is to find such control signal
- u that will minimize the following performance criteria: J = inetgral ( y'Qy + u'Ru)dt, where ' means trasnpose operation. Optimal LQR control minimize both energies terms (one with Q and other with R). I have found this statement: "LQR is a trade-off because decreasing the energy of the output will require a large control signal and a small control signal will lead to large outputs. The role of the weighting matrices Q and R is to establish a trade-off between these conflicting goals".
I'm not really sure, how to interpret this. Can you explain in more details, why small control signal will lead to large outputs? This is not obvious to me. Any help is highy appreciated.