Stabilization of nonlinear systems by similarity transformations
For a system , , , where the pair is given, we obtain the feedback vector to stabilize the corresponding closed loop system. For an arbitrarily chosen constant vector , a sufficient condition of the existence and an explicit form of a similarity transformation is established. The latter transforms matrix into the Frobenius matrix, vector into , and an unknown feedback vector into the first unit vector. The boundaries of are determined by the boundaries of , . The stabilization of the transformed system is subject to the choice of the constant vector .