A suboptimal controller for minimun sensitivity of closed loop eigenvalues to parameter variations

The design of a suboptimal controller for linear time invariant multivariable systems, which assigns the closed loop eigenvalues at desired locations and minimizes their sensitivity with respect to plant parameters, is outlined. The dominant open loop poles are shifted in groups employing a dyadic structure of state feedback for each group. Freedom available in choosing the constants of proportionality of the different rows of the dyadic matrices is used for eigenvalue sensitivity minimization. Since the final controller matrix is the sum of different dyadic matrices, the sensitivity of the final closed loop poles can be made less than that obtained by shifting all the dominant eigenvalues in one stage using unity rank feedback. An example illustrating the design method is given.