The transferability of bounded initial regions by feedback compensation

The problem of transferring all members of a bounded initial set to a desired target set in fixed time is addressed. It is found that for (A, B) controllable, such a transfer is always possible via constant state variable feedback. Expansion of state in matrix Lagrange polynomials enables one to develop a synthesis algorithm to obtain the appropriate feedback. The feedback synthesis procedure is exemplified for a 3-dimenaional unstable plant where the problem of stabilizability in prespecified time is considered as a special case of the above.