Pole placement optimization for SISO control system

We consider the control design problem for a linear time-invariant plant. A linear controller is found that minimizes some system performance index, for example, the ratio of the plant output to the external disturbance, as the $H_{\infty }$-norm of the corresponding function, provided that the requirements for the system performance are satisfied, namely, those on the stability margin radius, the ratio of the control signal to the noise in measurements of the plant output, the damping ratio, and speed of response. The well-known control design methods from the Matlab Robust Control Toolbox package are considered for solving such a problem. A control design method is proposed that uses the roots of the characteristic polynomial of the closed-loop system as the variables to be varied in the standard optimization procedure and the standard pole placement procedure for obtaining the values of the controller coefficients.