On pole assignment in linear systems with incomplete state feedback

The following system is considered: where is an vector describing the state of the system, is an vector of inputs to the system, and is an vector ( ) of output variables. It is shown that if rank , and if (A,B) are controllable, then a linear feedback of the output variables u = K^*y, where K^*is a constant matrix, can always be found, so that eigenvalues of the closed-loop system matrix A + BK^*C are arbitrarily close (but not necessarily equal) to preassigned values. (The preassigned values must be chosen so that any complex numbers appearing do so in complex conjugate pairs.) This generalizes an earlier result of Wonham [1]. An algorithm is described which enables K^*to be simply found, and examples of the algorithm applied to some simple systems are included.