Construction of the Minimum Phase Systems and the Problem of Stabilization

For the affine system with vector control, the problem of stabilization of the zero equilibrium position can be solved by stabilizing the zero output value, provided that the affine system is a minimum phase one. The minimum phase systems enable essential extension of the set of stabilizing feedbacks. In order to make use of this approach in the problem of stabilization of the stationary point of the multidimensional affine system, one needs a virtual vector output such that the system is a minimum phase one. Existence of conditions for these virtual vector outputs and a method for their determination were presented. Virtual output-based stabilization is attained by constructing the Lyapunov function for a closed-loop system.