Robust stabilization of non-linear systems

Abstract

Abstract The problem of stabilizing a non-linear system whose parameters are not accurately known is discussed. Specifically, it is assumed that the non-linear system σ that needs to be stabilized has a recursive representation of the form x k + 1 =f(x k , u k ), where only a nominal description of the recursion function f is given, and where the actual recursion function may deviate from the nominal one. An explicit procedure for the stabilization of the system σ is derived. The procedure consists of the construction of a pair of dynamic compensators—a precompensator and a feedback compensator—which, when connected in a closed loop around the system σ, yield an internally stable control configuration. This configuration maintains its internal stability as long as the deviation of the recursion function f from nominality is within certain bounds. The compensators consist of recursive systems that can be readily implemented, and which are derived in an explicit form in terms of the nominal recursion function of the system Σ.