On the design of output regulators for nonlinear systems

This paper considers the output regulation problem for nonlinear systems. B y adding the assumption that the decoupling matrix of the system under cons ideration has maximum rank, the general results presented in Isidori and By rnes (IEEE Trans. Automat. Control 35(2) (1990) 131-140) have been improved in three ways. Firstly, the precise form of the regulators is presented fo r multi-input multi-output affine nonlinear systems. Secondly, the number o f unknown functions in the controller parameterization has been reduced. Fi nally, by introducing a hyperbolic realization and constructing auxiliary s ystems, a sufficient and generically necessary condition for the existence of the unknown functions is obtained. This condition is easily verifiable u sing only algebraic computation. These results provide a complete solution to the output regulation problem, for a dass of nonlinear systems. It is al so shown that for this class of systems, the output regulation problem is a lways generically solvable. (C) 2001 Elsevier Science B.V. All rights reser ved.