Design of full order unknown input observers with H∞ performance

In real world observation problems it may happen that, given a linear time invariant system, the classical unknown input observers theory cannot guarantee a complete decoupling between the estimation errors and the unknown inputs. However, there is some degree of freedom that may be used to minimize, in some sense, the remaining effect of the disturbance inputs. In this paper we propose a procedure that allows one to design an unknown input observer decoupling, where possible, the disturbance input from the estimation error, and minimising the effect of the remaining disturbances in an H_∞ sense. The design procedure is formulated in terms of linear matrix inequalities; if a feasible solution exists, such. a procedure also guarantees a desired rate of convergence for the estimation dynamics.