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

Abstract

AbstractThis 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 onthe 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.