Observers for bilinear systems with bounded input†

Abstract

The problem of designing state observers for time-invariant bilinear dynamical systems with bounded input is considered. Full order and reduced order observers are studied, both having a bilinear structure. A classical Liapunov method is applied to ensure uniform asymptotic stability of the observation error dynamics. An algorithmic criterion is derived for the existence of a stabilizing observer feedback matrix, involving the computation of the maximal solution of an algebraic Riccati equation, and checking for its positive definiteness. Subsequently a design procedure is presented. The influence of the main design parameters on the solvability of the Riccati equation and on the resulting feedback matrix is investigated. The required magnitude of feedback amplification may be traded off against the bounds on the input function.