Optimal stationary feedback control with specified relative stability

The paper presents a systematic procedure for designing optimal feedback control systems with the poles restricted either to the left of the line Re(s) =¿¿ or in a cone tan¿1{Im(s)/Re(s)} =±¿. Simple transformations of the complex variable s are utilised to find a characteristic polynomial for the desired closed-loop system. It is then shown that this polynomial can be used with the frequency-domain optimality condition and the observability condition to find a proper quadratic index. It is also shown that it may be necessary to include a product of the control variable and the state variable in the quadratic index so that arbitrary pole placement may be possible.