Explicit constructions of global stabilization and nonlinear H ∞ control laws for a class of nonminimum phase nonlinear multivariable systems

Abstract

This paper investigates a global stabilization problem and a nonlinear H∞ control problem for a class of nonminimum phase nonlinear multivariable systems. To avoid the complicated recursive design procedure, an asymptotic time-scale and eigenstructure assignment method is adopted to construct the control laws for the stabilization problem and the nonlinear H∞ control problem. A sufficient solvability condition is established on the unstable zero dynamics of the system for global stabilization problem and nonlinear H∞ control problem, respectively. Moreover, based on the sufficient solvability condition, an upper bound of the achievable L2-gain is estimated for the nonlinear H∞ control problem. Copyright © 2007 John Wiley & Sons, Ltd.