Explicit construction of H∞ control law for a class of nonminimum phase nonlinear multivariable systems

This paper addresses a nonlinear H∞ control problem for a class of nonminimum phase nonlinear multivariable systems. To avoid the complicated recursive design procedure, the asymptotic time-scale and eigenstructure assignment method is adopted to construct the control law for the nonlinear H∞ control problem. A sufficient solvability condition is established on the unstable zero-dynamics of the system for the nonlinear H∞ control problem. Moreover, based on the sufficient solvability condition, an upper bound of the achievable L2 gain is estimated for the nonlinear H∞ control problem.