Explicit Construction of Global Stabilization Control Law for a Class of Nonminimum Phase Nonlinear Multivariable Systems

This paper investigates a global stabilization problem for a class of nonminimum phase nonlinear multivariable systems. The nonlinearities of the system, which depend on the system output, can be unknown, but satisfy some linear growth conditions. The given system is first transformed into a special coordinate basis form, in which the system zero dynamics is divided into a stable part and an unstable part. A sufficient solvability condition is established on the unstable zero-dynamics of the system. To avoid the complicated recursive design procedure, the asymptotic time-scale and eigenstructure assignment method is adopted to construct the control law for the stabilization problem.